What is the derivative of f(x)=cos^3(x^2)2 ?

The derivative of f(x)=cos^3(x^2)2 is -12xcos^2(x^2)sin(x^2)

What is the first derivative of f(x)=cos^3(x^2)2 ?

The first derivative of f(x)=cos^3(x^2)2 is -12xcos^2(x^2)sin(x^2)

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derivative of

f (x) = cos^{3} (x^{2}) 2

- 12 x cos^{2} (x^{2}) sin (x^{2})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

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

Simplify

= - 12 x cos^{2} (x^{2}) sin (x^{2})

\frac{1}{sin ^{2} ( 3 x )}

y = 8 x - 5

5 x^{4} + 8

ln^{2} (x^{3}) - 3

(x^{2} + 2 x)^{\frac{1}{2}}

What is the derivative of f(x)=cos^3(x^2)2 ?
The derivative of f(x)=cos^3(x^2)2 is -12xcos^2(x^2)sin(x^2)
What is the first derivative of f(x)=cos^3(x^2)2 ?
The first derivative of f(x)=cos^3(x^2)2 is -12xcos^2(x^2)sin(x^2)