What is (\partial)/(\partial x)(cos^7(x^9y^5)) ?

The answer to (\partial)/(\partial x)(cos^7(x^9y^5)) is -63x^8y^5cos^6(x^9y^5)sin(x^9y^5)

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(\partial)/(\partial x)(cos^7(x^9y^5))

\frac{\partial}{\partial x} (cos^{7} (x^{9} y^{5}))

- 63 x^{8} y^{5} cos^{6} (x^{9} y^{5}) sin (x^{9} y^{5})

Solution steps

\frac{\partial}{\partial x} (cos^{7} (x^{9} y^{5}))

Treat

y

as a constant

Apply the chain rule:

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

= 7 (cos (x^{9} y^{5}))^{6} \frac{\partial}{\partial x} (cos (x^{9} y^{5}))

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

= 7 (cos (x^{9} y^{5}))^{6} (- sin (x^{9} y^{5}) \cdot 9 y^{5} x^{8})

Simplify

= - 63 x^{8} y^{5} cos^{6} (x^{9} y^{5}) sin (x^{9} y^{5})

y = \frac{4 - x e ^{x}}{x + e ^{x}}

\int x^{2} \frac{1}{x} d x

\int_{4}^{7} \frac{1}{x ^{2} - 1} d x

\frac{d y}{d x} = 6 x + 2

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

What is (\partial)/(\partial x)(cos^7(x^9y^5)) ?
The answer to (\partial)/(\partial x)(cos^7(x^9y^5)) is -63x^8y^5cos^6(x^9y^5)sin(x^9y^5)