What is (\partial)/(\partial x)(cos^5(x^3y^9)) ?

The answer to (\partial)/(\partial x)(cos^5(x^3y^9)) is -15x^2y^9cos^4(x^3y^9)sin(x^3y^9)

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(\partial)/(\partial x)(cos^5(x^3y^9))

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{9}))

- 15 x^{2} y^{9} cos^{4} (x^{3} y^{9}) sin (x^{3} y^{9})

Solution steps

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{9}))

Treat

y

as a constant

Apply the chain rule:

5 (cos (x^{3} y^{9}))^{4} \frac{\partial}{\partial x} (cos (x^{3} y^{9}))

= 5 (cos (x^{3} y^{9}))^{4} \frac{\partial}{\partial x} (cos (x^{3} y^{9}))

\frac{\partial}{\partial x} (cos (x^{3} y^{9})) = - sin (x^{3} y^{9}) \cdot 3 y^{9} x^{2}

= 5 (cos (x^{3} y^{9}))^{4} (- sin (x^{3} y^{9}) \cdot 3 y^{9} x^{2})

Simplify

= - 15 x^{2} y^{9} cos^{4} (x^{3} y^{9}) sin (x^{3} y^{9})

\frac{d}{d x} ((x^{4} + x^{3} + 1) (x^{2} - 2))

\int \frac{36 + x ^{2}}{x} d x

\int_{- 9}^{- 5} \frac{1}{x} d x

\int_{0}^{5} (6 e^{0.2 x} + 2 x) d x

f (x) = \frac{5}{x ^{3}} - \frac{4}{x ^{2}} + \frac{1}{x}

What is (\partial)/(\partial x)(cos^5(x^3y^9)) ?
The answer to (\partial)/(\partial x)(cos^5(x^3y^9)) is -15x^2y^9cos^4(x^3y^9)sin(x^3y^9)