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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
What is 6x plus 5 equals 95-3x?
6x + 5 = 95 - 3x The main goal is to get "x" by itself. So you can first subtract 5 from both sides because whatever you do on one side of the equation, you do to the other side.
6x = 90 - 3x Next add 3x on both sides.
9x = 90 Last divide by 9 on both sides.
x = 10
What is the derivative of fx equals x to the power of 2 over x plus 2?
That is the quotient rule and your function is....
f(x) = X^2/x+2
= (x+2)*2x-x^2*1/(x+2)^2
= 2x^2+4x-x^2/(x+2)^2
= x^2 + 4x/(x+2)^2
How do i solve Y squared equals negative 3 x?
That depends on what you want to "solve" it for. Do you want to plot it on a graph? Are you looking for the value of y with respect to x? The value of x with respect to y? The derivative of each? The integral of each? You need to clarify your question.
In answer to all of those interpretations:
- It describes a horizontally aligned parabola that proceeds indefinitely to the "left" (ie. negative) whose vertex lies at the point 0, 0
- y = (-3x)1/2
- dy/dx = (-3x/2)-1/2
- ∫(-3x)1/2 dx = (-x/2)3/2 + C
- x = -y2/3
- dx/dy = -2y/3
- ∫(-y2/3) dy = -y3/9 + C
Can't be done unless you have another equation with the same x and y. Then you would solve for simultaneous equations.
What is the answer to negative three x plus y equals twelve?
This is an equation of a straight line: y = 3x + 12, which passes through the point (0,12) and has a slope of 3 {for every 1 unit increase in x, y increases by 3}
What is the answer to -8x plus 7 equals 4x - 5?
-8X + 7 = 4X - 5
add -8X to both sides
7 = 12X - 5
add 5 to each side
12 = 12X
divide each side by 12
1 = X
check
-8(1) + 7 = 4(1) - 5
-1 = -1
checks
How do you solve x2 equals 7-4?
If you actually meant that as you wrote it:
x2 = 7 - 4
Then the answer is simple:
x2 = 7 - 4
∴ x2 = 3
∴ x = √3
If on the other hand, you actually wanted to say:
x2 = 7x - 4
Then you can find it this way:
x2 = 7x - 4
∴ x - 7x = -4
∴ x - 7x + (7/2)2 = -4 + (7/2)2
∴ (x - 7/2)2 = -16/4 + 49/4
∴ x - 7/2 = ± √(33/4)
∴ x = 7/2 ± √33/2
∴ x = (7 ± √33) / 2
Alternatively, if you meant to say:
x2 = 7 - 4x
Then the answer is:
x2 = 7 - 4x
∴ x2 + 4x = 7
∴ x2 + 4x + 4 = 7
∴ (x + 2)2 = 7
∴ x + 2 = ± √7
∴ x = -2 ± √7
How do i sketch f(x)4-x...x-1 then find f(-3)?
You take different values of x, calculate f(x) for each of these values and then plot the points [x, f(x)] on the coordinate plane. To find f(-3) you could read off the value of the graph, ie f(x) when x = -3. Alternatively, you could substitute x = -3 in the equation for f(x).
Since the question posted contains an ellipsis, the specific question is unknown and so there is no way to answer it.
Differentiation Rules and examples and explanation?
Differentiating is the act of finding the derivative of a function, thus allowing you to find out how the function changes as its input changes, such as finding the rate of change of the gradient of the function, and when differentiating with respect to time can allow you to give equations explaining the motion of various objects, depending on how you differentiate the functions. There are two main types of differentiation, ordinary differentiation and partial differentiation, the rules outlined below are for ordinary differentiation. While the rules for partial differentiation are not that dissimilar, they do not need to be known outside of university level mathematics and physics.
(using f' and g' to denote the derivative of the functions f and g of x respectively, x is a variable, o indicates a composite function, all other letters are constants, rules in bold are important)
Elementary rulesf = xn, f' = nx(n-1) elementary power rule
f = a, f' = 0 constant rule
f = ax, f' = a derivative of a linear function is a constant
(af +bg)' = af'+bg' linearity of differentiation, leading to the 3 following,
(af)' = af' constant multiple rule
(f+g)' = f'+g' sum rule
(f-g)' = f'-g' subtraction rule,
(fg)' = f'g + fg' product rule
(fog)' = (f(g))' = (f'(g))g' = (f'og)g' chain rule
f = 1/g, f' = -g'/g2 reciprocal rule
(f/g)' = (f'g-fg')/g2 quotient rule
f=sin(x), f'=cos(x)
f=cos(x), f'=-sin(x)
f=tan(x), f'=sec2(x)
f=sec(x), f'=sec(x)tan(x)
f=cosec(x) f'=-cosec(x)cot(x)
f=cot(x), f'=-cosec2(x)
f=exp(ax), f'=a*exp(ax)
f=exp(axn), f'=anx(n-1)*exp(axn)
f=ax, f'=(log(a))*ax
f=log(x), f'=1/x
f=log(xn), f'=nx(n-1)/xn
f=xx, f'=xx(1+log(x))
these are just the simple rules of differentiation for various functions, there are a LOT more, but they are generally only of use at university levels.
Where should the parentheses in 7 plus 7 x 3 equals 4 x 7?
7+(7*3) because 7*3=21 and 21+7=28, which is equal to 28, the product of 4*7.
What is the ordered pair for y equals -2x plus 4?
There are an infinite number of ordered pairs.
Any point on the straight line which passes through (0,4) and has a gradient of -2 will be an ordered pair for the equation.
