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

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

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

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

- 24 x^{5} y^{5} cos^{3} (x^{6} y^{5}) sin (x^{6} y^{5})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

4 (cos (x^{6} y^{5}))^{3} \frac{\partial}{\partial x} (cos (x^{6} y^{5}))

= 4 (cos (x^{6} y^{5}))^{3} \frac{\partial}{\partial x} (cos (x^{6} y^{5}))

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

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

Simplify

= - 24 x^{5} y^{5} cos^{3} (x^{6} y^{5}) sin (x^{6} y^{5})

y = 2 x^{2} + 6 x + 5

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

\int_{1}^{3} x 4^{x^{2}} d x

\int \frac{1 - x ^{2}}{x ^{4}} arcsin (x) d x

\frac{\partial}{\partial t} (sin (2 t))

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