What is the derivative of cos^4(2x^3-5) ?

The derivative of cos^4(2x^3-5) is -24x^2cos^3(2x^3-5)sin(2x^3-5)

What is the first derivative of cos^4(2x^3-5) ?

The first derivative of cos^4(2x^3-5) is -24x^2cos^3(2x^3-5)sin(2x^3-5)

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\frac{d}{d x} (cos^{4} (2 x^{3} - 5))

- 24 x^{2} cos^{3} (2 x^{3} - 5) sin (2 x^{3} - 5)

Solution steps

\frac{d}{d x} (cos^{4} (2 x^{3} - 5))

Apply the chain rule:

4 (cos (2 x^{3} - 5))^{3} \frac{d}{d x} (cos (2 x^{3} - 5))

= 4 (cos (2 x^{3} - 5))^{3} \frac{d}{d x} (cos (2 x^{3} - 5))

\frac{d}{d x} (cos (2 x^{3} - 5)) = - sin (2 x^{3} - 5) \cdot 6 x^{2}

= 4 (cos (2 x^{3} - 5))^{3} (- sin (2 x^{3} - 5) \cdot 6 x^{2})

Simplify

= - 24 x^{2} cos^{3} (2 x^{3} - 5) sin (2 x^{3} - 5)

\int \frac{5 - 2 x ^{2}}{y ^{2}} d y

\int sin (10 x) d x

y = x (x + 3) (x - 4), x = 0

(5 e^{x})^{^{'}}

x \to 0 lim (\frac{1}{tan ( x )})

What is the derivative of cos^4(2x^3-5) ?
The derivative of cos^4(2x^3-5) is -24x^2cos^3(2x^3-5)sin(2x^3-5)
What is the first derivative of cos^4(2x^3-5) ?
The first derivative of cos^4(2x^3-5) is -24x^2cos^3(2x^3-5)sin(2x^3-5)