What is (\partial)/(\partial x)(cos^4(x^8y^7)) ?

The answer to (\partial)/(\partial x)(cos^4(x^8y^7)) is -32x^7y^7cos^3(x^8y^7)sin(x^8y^7)

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(\partial)/(\partial x)(cos^4(x^8y^7))

\frac{\partial}{\partial x} (cos^{4} (x^{8} y^{7}))

- 32 x^{7} y^{7} cos^{3} (x^{8} y^{7}) sin (x^{8} y^{7})

Solution steps

\frac{\partial}{\partial x} (cos^{4} (x^{8} y^{7}))

Treat

y

as a constant

Apply the chain rule:

4 (cos (x^{8} y^{7}))^{3} \frac{\partial}{\partial x} (cos (x^{8} y^{7}))

= 4 (cos (x^{8} y^{7}))^{3} \frac{\partial}{\partial x} (cos (x^{8} y^{7}))

\frac{\partial}{\partial x} (cos (x^{8} y^{7})) = - sin (x^{8} y^{7}) \cdot 8 y^{7} x^{7}

= 4 (cos (x^{8} y^{7}))^{3} (- sin (x^{8} y^{7}) \cdot 8 y^{7} x^{7})

Simplify

= - 32 x^{7} y^{7} cos^{3} (x^{8} y^{7}) sin (x^{8} y^{7})

\int e^{- c o s (x)} sin (x) d x

\frac{\partial}{\partial x} (\frac{1}{4 x})

\frac{\partial}{\partial x} (3 x e^{7 x y})

\int_{0}^{7} \frac{4 t}{( t - 8 ) ^{2}} d t

n = 0 \sum \infty \frac{1}{n ^{3}}

What is (\partial)/(\partial x)(cos^4(x^8y^7)) ?
The answer to (\partial)/(\partial x)(cos^4(x^8y^7)) is -32x^7y^7cos^3(x^8y^7)sin(x^8y^7)