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The derivative with respect to 'x' of sin(pi x) ispi cos(pi x)
The derivative of sin(x) is cos(x).
Every fourth derivative, you get back to "sin x" - in other words, the 84th derivative of "sin x" is also "sin x". From there, you need to take the derivative 3 more times, getting:85th derivative: cos x86th derivative: -sin x87th derivative: -cos x
The derivative of cos(x) is negative sin(x). Also, the derivative of sin(x) is cos(x).
To differentiate y=sin(sin(x)) you need to use the chain rule. A common way to remember the chain rule is "derivative of the outside, keep the inside, derivative of the inside". First, you take the derivative of the outside. The derivative of sin is cos. Then, you keep the inside, so you keep sin(x). Then, you multiple by the derivative of the inside. Again, the derivative of sinx is cosx. In the end, you get y'=cos(sin(x))cos(x))
Generally, the derivative of sine is cosine.
The derivative of (sin (theta))^.5 is (cos(theta))/(2sin(theta))
Derivative of sin x = cos x, so chain rule to derive 8x = 8 , answer is 8cos8x
The derivative of sin (x) is cos (x). It does not work the other way around, though. The derivative of cos (x) is -sin (x).
The derivative of cos(x) equals -sin(x); therefore, the anti-derivative of -sin(x) equals cos(x).
Y=10^sin(x) The derivative is: (log(5)+log(2))*cos(x)*2^sin(x)*5^sin(x) Use the chain rule, product rule, and power rules combined with sin(x) rule.
d/dx (-cscx-sinx)=cscxcotx-cosx