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

The answer to (\partial)/(\partial x)(cos^7(x^6y^6)) is -42x^5y^6cos^6(x^6y^6)sin(x^6y^6)

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

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

- 42 x^{5} y^{6} cos^{6} (x^{6} y^{6}) sin (x^{6} y^{6})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (cos (x^{6} y^{6})) = - sin (x^{6} y^{6}) \cdot 6 y^{6} x^{5}

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

Simplify

= - 42 x^{5} y^{6} cos^{6} (x^{6} y^{6}) sin (x^{6} y^{6})

\frac{d}{d x} (2 sin (2 x) - ln (3 x + 1))

\int \frac{8 ln ( x )}{x ^{2}} d x

\frac{d}{d x} (\frac{( 40 x ^{5} )}{e ^{x}})

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 4

\frac{\partial}{\partial x} (x ln (x y))

What is (\partial)/(\partial x)(cos^7(x^6y^6)) ?
The answer to (\partial)/(\partial x)(cos^7(x^6y^6)) is -42x^5y^6cos^6(x^6y^6)sin(x^6y^6)