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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
If x equals 8 then 4x plus 6 equals 46?
No.
Substitute the value 8 for x, and you have 4x +6 = 4(8) +6 = 32 +6 = 38.
What is the derivative of cos x raised to the x?
cos(xx)?
d/dx(cosu)=-sin(u)*d/dx(u)
d/dx(cos(xx))=-sin(xx)*d/dx(xx)
-The derivative of xx is:
y=xx ;You have to use implicit derivation because there is no formula for taking the derivative of uu.
lny=lnxx
lny=xlnx
-The derivative of lnx is:
d/dx(lnu)=(1/u)*d/dx(u)
-d/dx(uv)= u*dv/dx+v*du/dx
Therefore:
(1/y)*dy/dx=x*[(1/x)*d/dx(x)]+lnx(d/dx(x))
-The derivative of x is:
d/dx(xn)=nxn-1
d/dx(x)=1*x1-1
d/dx(x)=1*x0
d/dx(x)=1*(1)
d/dx(x)=1
(1/y)*dy/dx=x*[(1/x)*(1)]+lnx(1)
(1/y)*dy/dx=x*[(1/x)]+lnx
(1/y)*dy/dx=(x/x)+lnx
(1/y)*dy/dx=1+lnx
dy/dx=y(1+lnx) ;Multiply y to both sides
dy/dx=xx(1+lnx) ;y=xx, so replace the y with xx
d/dx(cos(xx))=-sin(xx)*[xx*(1+lnx)]
d/dx(cos(xx))=-(1+lnx)*xx*sin(xx)
(cosx)x?
Again with the implicit derivation:
y=(cosx)x
lny=x*ln(cosx)
(1/y)*dy/dx=x[d/dx(lncosx)]+lncosx(d/dx(x))
(1/y)*dy/dx=x[(1/cosx)*(-sinx)(1)]+lncosx(1) ;The derivative of lncosx is (1/cosx)*d/dx(cosx). The derivative of cosx is (-sinx)*d/dx (x). The derivative of x is 1.
(1/y)*dy/dx=x[(1/cosx)*(-sinx)]+lncosx
(1/y)*dy/dx=x[-tanx]+lncosx
(1/y)*dy/dx=-xtanx+lncosx
dy/dx=y(-xtanx+lncosx) ;Multiply both sides by y
dy/dx=(cosx)x(-xtanx+lncosx) ;y=(cosx)x, replace all y's with (cosx)x
dy/dx=(cosx)x(-xtanx+lncosx)=(cosx)x-1(cosx*lncosx-xsinx)
How do you factor 4x squared 8?
That depends on what you're doing to the 8.
It's either 4(x2 + 2) or 4(x2 - 2)
27 multiplied by 3 is 81. Calculators might also help for similar problems.
If you put the equation into standard form, ax2 + bx + c = 0, then the number and type of roots are determined by the expression b2 - 4ac - this is because in the quadratic equation, this appears under a radical sign. If this expression is...
- Positive: the equation has two real solutions.
- Zero: the equation has one solution, sometimes considered a "double root".
- Negative: the equation has two complex solutions.
What is x if x over 5 equals 9 over 15?
x=3 cross multiply and you get 15x=45 then divide 45 by 15 and you get 3
Is the equation of a straight line with slope 2 and an intercept of (0,20).
It's a simple linear equation in 'y'.
It can be solved like this:
6y + 20 = 9
Subtract 20 from each side:
6y = -11
Divide each side by 6:
y = -11/6
What is the answer to solve by elimination x plus 2y equals 0?
The answer is that it cannot be done. To solve a set of equations in k variables (in this case, 2) you need at least two independent equations.
What is the importance about X Y Z affair?
During the Quasi-War, the XYZ Affair damaged relations between America and France.
Solve e raised to the power of negative x equals 6?
e-x = 6Take the natural log of both sides:
ln(e-x) = ln(6)
-x = ln(6)
x = -ln(6)So x = -ln(6), which is about -1.792.
How do you solve linear combination 5x equals 4y-30 and 2x plus 3y equals -12?
Here is one possible method of solving the system: 5x = 4y - 30
2x + 3y = -12
Rewrite to line up variables:
5x - 4y = -30
2x + 3y = -12
Multiply the top equation by 2 and the bottom equation by 5:
10x - 8y = -60
10x + 15y = -60
Subtract the two equations:
-23y = 0;
So y = 0; plug back into an original equation to find x:
2x + 3(0) = -12
2x = -12
x = -6The solution to the system is x = -6 and y = 0, or the point (-6,0).
What does it mean if an equation is simplified to 0 0 do all problems have exactly one solution?
An equation that is simplified to 0 0 is called a perfect equation. It usually have exactly one solution.
