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

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

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

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

- 48 x^{7} y^{6} cos^{5} (x^{8} y^{6}) sin (x^{8} y^{6})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= - 48 x^{7} y^{6} cos^{5} (x^{8} y^{6}) sin (x^{8} y^{6})

y = 2 x - x^{2}, y = 2 x - 4

x \to 9 lim \frac{( x ^{\frac{1}{2}} - 3 ) ( x + 1 )}{x ^{2} - 8 x - 9}

y = (3 x^{2} - 2 x - 4) 5^{x}

\int \frac{5000 ln ( x + 20 )}{( x + 20 ) ^{2}} d x

\frac{d}{d x} (- 5 e^{3 x})

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