What is (\partial)/(\partial x)(cos^7(x^4y^6)) ?

The answer to (\partial)/(\partial x)(cos^7(x^4y^6)) is -28x^3y^6cos^6(x^4y^6)sin(x^4y^6)

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(\partial)/(\partial x)(cos^7(x^4y^6))

\frac{\partial}{\partial x} (cos^{7} (x^{4} y^{6}))

- 28 x^{3} y^{6} cos^{6} (x^{4} y^{6}) sin (x^{4} y^{6})

Solution steps

\frac{\partial}{\partial x} (cos^{7} (x^{4} y^{6}))

Treat

y

as a constant

Apply the chain rule:

7 (cos (x^{4} y^{6}))^{6} \frac{\partial}{\partial x} (cos (x^{4} y^{6}))

= 7 (cos (x^{4} y^{6}))^{6} \frac{\partial}{\partial x} (cos (x^{4} y^{6}))

\frac{\partial}{\partial x} (cos (x^{4} y^{6})) = - sin (x^{4} y^{6}) \cdot 4 y^{6} x^{3}

= 7 (cos (x^{4} y^{6}))^{6} (- sin (x^{4} y^{6}) \cdot 4 y^{6} x^{3})

Simplify

= - 28 x^{3} y^{6} cos^{6} (x^{4} y^{6}) sin (x^{4} y^{6})

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\frac{\partial}{\partial x} (13.12 + 0.6215 x - 11.37 y^{0.16} + 0.3965 x y^{0.16})

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What is (\partial)/(\partial x)(cos^7(x^4y^6)) ?
The answer to (\partial)/(\partial x)(cos^7(x^4y^6)) is -28x^3y^6cos^6(x^4y^6)sin(x^4y^6)