What is (\partial)/(\partial x)(cos^5(x^7y^5)) ?

The answer to (\partial)/(\partial x)(cos^5(x^7y^5)) is -35x^6y^5cos^4(x^7y^5)sin(x^7y^5)

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(\partial)/(\partial x)(cos^5(x^7y^5))

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

- 35 x^{6} y^{5} cos^{4} (x^{7} y^{5}) sin (x^{7} y^{5})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

5 (cos (x^{7} y^{5}))^{4} \frac{\partial}{\partial x} (cos (x^{7} y^{5}))

= 5 (cos (x^{7} y^{5}))^{4} \frac{\partial}{\partial x} (cos (x^{7} y^{5}))

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

= 5 (cos (x^{7} y^{5}))^{4} (- sin (x^{7} y^{5}) \cdot 7 y^{5} x^{6})

Simplify

= - 35 x^{6} y^{5} cos^{4} (x^{7} y^{5}) sin (x^{7} y^{5})

x y^{^{'}} + (1 - x) y = 0

\frac{d N}{d t} = N (1 - 0.0005 N)

x \frac{d y}{d x} + y = (x y)^{\frac{3}{2}}

\frac{d}{d x} (y - x n (y + x))

\frac{\partial}{\partial y} (x - y - 1)

What is (\partial)/(\partial x)(cos^5(x^7y^5)) ?
The answer to (\partial)/(\partial x)(cos^5(x^7y^5)) is -35x^6y^5cos^4(x^7y^5)sin(x^7y^5)