What is the derivative of-5cos(cos(x^6)) ?

The derivative of-5cos(cos(x^6)) is -30x^5sin(cos(x^6))sin(x^6)

What is the first derivative of-5cos(cos(x^6)) ?

The first derivative of-5cos(cos(x^6)) is -30x^5sin(cos(x^6))sin(x^6)

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\frac{d}{d x} (- 5 cos (cos (x^{6})))

- 30 x^{5} sin (cos (x^{6})) sin (x^{6})

Solution steps

\frac{d}{d x} (- 5 cos (cos (x^{6})))

Take the constant out:

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

= - 5 \frac{d}{d x} (cos (cos (x^{6})))

Apply the chain rule:

- sin (cos (x^{6})) \frac{d}{d x} (cos (x^{6}))

= - sin (cos (x^{6})) \frac{d}{d x} (cos (x^{6}))

\frac{d}{d x} (cos (x^{6})) = - sin (x^{6}) \cdot 6 x^{5}

= - 5 (- sin (cos (x^{6})) (- sin (x^{6}) \cdot 6 x^{5}))

Simplify

= - 30 x^{5} sin (cos (x^{6})) sin (x^{6})

What is the derivative of-5cos(cos(x^6)) ?
The derivative of-5cos(cos(x^6)) is -30x^5sin(cos(x^6))sin(x^6)
What is the first derivative of-5cos(cos(x^6)) ?
The first derivative of-5cos(cos(x^6)) is -30x^5sin(cos(x^6))sin(x^6)