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

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

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

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

- 63 x^{6} y^{9} cos^{8} (x^{7} y^{9}) sin (x^{7} y^{9})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

9 (cos (x^{7} y^{9}))^{8} \frac{\partial}{\partial x} (cos (x^{7} y^{9}))

= 9 (cos (x^{7} y^{9}))^{8} \frac{\partial}{\partial x} (cos (x^{7} y^{9}))

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

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

Simplify

= - 63 x^{6} y^{9} cos^{8} (x^{7} y^{9}) sin (x^{7} y^{9})

y = 7 arctan (x + 1 + x^{2})

y = 5 x, y = \frac{5}{2} x, y = 84 - x^{2}

x \to 8 lim (ln (x - 8))

\int_{1}^{10} \frac{25}{x ^{3}} d x

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