What is (\partial)/(\partial x)(cos^6(y^7x^8)) ?

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

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(\partial)/(\partial x)(cos^6(y^7x^8))

\frac{\partial}{\partial x} (cos^{6} (y^{7} x^{8}))

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

Solution steps

\frac{\partial}{\partial x} (cos^{6} (y^{7} x^{8}))

Treat

y

as a constant

Apply the chain rule:

6 (cos (y^{7} x^{8}))^{5} \frac{\partial}{\partial x} (cos (y^{7} x^{8}))

= 6 (cos (y^{7} x^{8}))^{5} \frac{\partial}{\partial x} (cos (y^{7} x^{8}))

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

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

Simplify

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

x \to 0 lim (x^{3} sin (x^{1}))

arcsec (6 x)

\int \frac{1}{x ( x ^{2} - 100 ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial x} (ln (x^{0.6} y^{0.4}))

f (x) = x^{2} - x, at a = 1

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