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

The answer to (\partial)/(\partial x)(cos^9(x^8y^6)) is -72x^7y^6cos^8(x^8y^6)sin(x^8y^6)

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

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

- 72 x^{7} y^{6} cos^{8} (x^{8} y^{6}) sin (x^{8} y^{6})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (cos (x^{8} y^{6})) = - sin (x^{8} y^{6}) \cdot 8 y^{6} x^{7}

= 9 (cos (x^{8} y^{6}))^{8} (- sin (x^{8} y^{6}) \cdot 8 y^{6} x^{7})

Simplify

= - 72 x^{7} y^{6} cos^{8} (x^{8} y^{6}) sin (x^{8} y^{6})

4^{\frac{c}{x}}

\int sin^{3} (x co) s^{3} x d x

\int_{0}^{\infty} x e^{- \frac{x}{9}} d x

x \to \infty lim (- 3)

\frac{\partial}{\partial x} (\frac{3 x + 2 x y}{7 x + 6 y})

What is (\partial)/(\partial x)(cos^9(x^8y^6)) ?
The answer to (\partial)/(\partial x)(cos^9(x^8y^6)) is -72x^7y^6cos^8(x^8y^6)sin(x^8y^6)