What is (\partial)/(\partial x)(cos^6(x^4y^5)) ?

The answer to (\partial)/(\partial x)(cos^6(x^4y^5)) is -24x^3y^5cos^5(x^4y^5)sin(x^4y^5)

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(\partial)/(\partial x)(cos^6(x^4y^5))

\frac{\partial}{\partial x} (cos^{6} (x^{4} y^{5}))

- 24 x^{3} y^{5} cos^{5} (x^{4} y^{5}) sin (x^{4} y^{5})

Solution steps

\frac{\partial}{\partial x} (cos^{6} (x^{4} y^{5}))

Treat

y

as a constant

Apply the chain rule:

6 (cos (x^{4} y^{5}))^{5} \frac{\partial}{\partial x} (cos (x^{4} y^{5}))

= 6 (cos (x^{4} y^{5}))^{5} \frac{\partial}{\partial x} (cos (x^{4} y^{5}))

\frac{\partial}{\partial x} (cos (x^{4} y^{5})) = - sin (x^{4} y^{5}) \cdot 4 y^{5} x^{3}

= 6 (cos (x^{4} y^{5}))^{5} (- sin (x^{4} y^{5}) \cdot 4 y^{5} x^{3})

Simplify

= - 24 x^{3} y^{5} cos^{5} (x^{4} y^{5}) sin (x^{4} y^{5})

\int 2 + x^{2} d x

x^{3} - 10 x^{2} + 12 x + 3

\int \frac{3 x ^{4}}{2} - 4 x^{\frac{3}{2}} d x

f (x) = \frac{e ^{x} + e ^{- x}}{2}

\frac{d y}{d x} = \frac{5 x + 2 y}{5 x + 2 y + 2}

What is (\partial)/(\partial x)(cos^6(x^4y^5)) ?
The answer to (\partial)/(\partial x)(cos^6(x^4y^5)) is -24x^3y^5cos^5(x^4y^5)sin(x^4y^5)