What is (\partial)/(\partial x)(cos^5(x^3y^8)) ?

The answer to (\partial)/(\partial x)(cos^5(x^3y^8)) is -15x^2y^8cos^4(x^3y^8)sin(x^3y^8)

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(\partial)/(\partial x)(cos^5(x^3y^8))

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{8}))

- 15 x^{2} y^{8} cos^{4} (x^{3} y^{8}) sin (x^{3} y^{8})

Solution steps

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{8}))

Treat

y

as a constant

Apply the chain rule:

5 (cos (x^{3} y^{8}))^{4} \frac{\partial}{\partial x} (cos (x^{3} y^{8}))

= 5 (cos (x^{3} y^{8}))^{4} \frac{\partial}{\partial x} (cos (x^{3} y^{8}))

\frac{\partial}{\partial x} (cos (x^{3} y^{8})) = - sin (x^{3} y^{8}) \cdot 3 y^{8} x^{2}

= 5 (cos (x^{3} y^{8}))^{4} (- sin (x^{3} y^{8}) \cdot 3 y^{8} x^{2})

Simplify

= - 15 x^{2} y^{8} cos^{4} (x^{3} y^{8}) sin (x^{3} y^{8})

\frac{d ^{2} y}{d x ^{2}} = - y

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

x \to - 1 lim (∣ x ∣ - 3)

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

\frac{d}{d x} (x ln (2 x))

What is (\partial)/(\partial x)(cos^5(x^3y^8)) ?
The answer to (\partial)/(\partial x)(cos^5(x^3y^8)) is -15x^2y^8cos^4(x^3y^8)sin(x^3y^8)