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

The answer to (\partial)/(\partial x)(cos^6(x^8y^9)) is -48x^7y^9cos^5(x^8y^9)sin(x^8y^9)

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

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

- 48 x^{7} y^{9} cos^{5} (x^{8} y^{9}) sin (x^{8} y^{9})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= - 48 x^{7} y^{9} cos^{5} (x^{8} y^{9}) sin (x^{8} y^{9})

y^{^{''}} + 5 y^{^{'}} + 4 y = 0

\int \frac{10}{x ^{2}} d x

\frac{\partial}{\partial x} (7 e^{x} cos (yz))

x^{4} f (x)

(\frac{d y}{d x}) - 3 y = e^{2 x}

What is (\partial)/(\partial x)(cos^6(x^8y^9)) ?
The answer to (\partial)/(\partial x)(cos^6(x^8y^9)) is -48x^7y^9cos^5(x^8y^9)sin(x^8y^9)