What is the derivative of f(x)=cos^3(3x-1) ?

The derivative of f(x)=cos^3(3x-1) is -9cos^2(3x-1)sin(3x-1)

What is the first derivative of f(x)=cos^3(3x-1) ?

The first derivative of f(x)=cos^3(3x-1) is -9cos^2(3x-1)sin(3x-1)

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derivative of

f (x) = cos^{3} (3 x - 1)

- 9 cos^{2} (3 x - 1) sin (3 x - 1)

Solution steps

\frac{d}{d x} (cos^{3} (3 x - 1))

Apply the chain rule:

3 (cos (3 x - 1))^{2} \frac{d}{d x} (cos (3 x - 1))

= 3 (cos (3 x - 1))^{2} \frac{d}{d x} (cos (3 x - 1))

\frac{d}{d x} (cos (3 x - 1)) = - sin (3 x - 1) \cdot 3

= 3 (cos (3 x - 1))^{2} (- sin (3 x - 1) \cdot 3)

Simplify

= - 9 cos^{2} (3 x - 1) sin (3 x - 1)

What is the derivative of f(x)=cos^3(3x-1) ?
The derivative of f(x)=cos^3(3x-1) is -9cos^2(3x-1)sin(3x-1)
What is the first derivative of f(x)=cos^3(3x-1) ?
The first derivative of f(x)=cos^3(3x-1) is -9cos^2(3x-1)sin(3x-1)