Question

composite function of derivative find y=cos^3x​

Answer 1

Answer:

Step-by-step explanation:

The derivative of

cos^3(x) is equal to:

−3cos^2(x)•sin(x)

We can get this result using the Chain Rule which is a formula for computing the derivative of the composition of two or more functions in the form:

f(g(x)) .

We can see that the function g(x)

is nested inside the f(x) function.

Deriving we get:

derivative of f(g(x)) --> f'(g(x))•g'(x)

In this case the f() function is the cube or ()^3 while the second function "nested" into the cube is

cos(x) .

First we deal with the cube deriving it but letting the argument g(x) (i.e. the cos) untouched and then you multiply by the derivative of the nested function.

Derivative of this : () ^3 = 3() ^2

Derivative of : cos(x) = -sin(x)

Derivative of : cos^3(x) = 3cos^2(x)• -sin(x)

Which is equal to: −3cos^2(x)•sin(x)