What is (\partial)/(\partial x)(cos^3(1-5x^2)) ?

The answer to (\partial)/(\partial x)(cos^3(1-5x^2)) is 30xcos^2(1-5x^2)sin(1-5x^2)

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(\partial)/(\partial x)(cos^3(1-5x^2))

\frac{\partial}{\partial x} (cos^{3} (1 - 5 x^{2}))

30 x cos^{2} (1 - 5 x^{2}) sin (1 - 5 x^{2})

Solution steps

\frac{\partial}{\partial x} (cos^{3} (1 - 5 x^{2}))

Apply the chain rule:

3 (cos (1 - 5 x^{2}))^{2} \frac{\partial}{\partial x} (cos (1 - 5 x^{2}))

= 3 (cos (1 - 5 x^{2}))^{2} \frac{\partial}{\partial x} (cos (1 - 5 x^{2}))

\frac{\partial}{\partial x} (cos (1 - 5 x^{2})) = 10 x sin (1 - 5 x^{2})

= 3 (cos (1 - 5 x^{2}))^{2} \cdot 10 x sin (1 - 5 x^{2})

Simplify

= 30 x cos^{2} (1 - 5 x^{2}) sin (1 - 5 x^{2})

\frac{d y}{d x} = 5 y + 1

(\frac{x ^{2} + 8}{x ^{2} - 8})^{3}

\int \frac{1}{36 e ^{- 8 x} + e ^{8 x}} d x

\frac{\partial}{\partial x} (z e^{x + y} - x y)

\frac{d}{d x} ((x + 1) (x + 1 - \frac{1}{x + 2}))

What is (\partial)/(\partial x)(cos^3(1-5x^2)) ?
The answer to (\partial)/(\partial x)(cos^3(1-5x^2)) is 30xcos^2(1-5x^2)sin(1-5x^2)