What is (\partial)/(\partial x)(cos^6(x^9y^8)) ?

The answer to (\partial)/(\partial x)(cos^6(x^9y^8)) is -54x^8y^8cos^5(x^9y^8)sin(x^9y^8)

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(\partial)/(\partial x)(cos^6(x^9y^8))

\frac{\partial}{\partial x} (cos^{6} (x^{9} y^{8}))

- 54 x^{8} y^{8} cos^{5} (x^{9} y^{8}) sin (x^{9} y^{8})

Solution steps

\frac{\partial}{\partial x} (cos^{6} (x^{9} y^{8}))

Treat

y

as a constant

Apply the chain rule:

6 (cos (x^{9} y^{8}))^{5} \frac{\partial}{\partial x} (cos (x^{9} y^{8}))

= 6 (cos (x^{9} y^{8}))^{5} \frac{\partial}{\partial x} (cos (x^{9} y^{8}))

\frac{\partial}{\partial x} (cos (x^{9} y^{8})) = - sin (x^{9} y^{8}) \cdot 9 y^{8} x^{8}

= 6 (cos (x^{9} y^{8}))^{5} (- sin (x^{9} y^{8}) \cdot 9 y^{8} x^{8})

Simplify

= - 54 x^{8} y^{8} cos^{5} (x^{9} y^{8}) sin (x^{9} y^{8})

\frac{\partial}{\partial x} (ln (x^{4} + y^{9}))

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

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

\int \frac{( x + 1 ) ^{4}}{2 x} d x

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

What is (\partial)/(\partial x)(cos^6(x^9y^8)) ?
The answer to (\partial)/(\partial x)(cos^6(x^9y^8)) is -54x^8y^8cos^5(x^9y^8)sin(x^9y^8)