What is (\partial)/(\partial x)(cos^4(x^3y^8)) ?

The answer to (\partial)/(\partial x)(cos^4(x^3y^8)) is -12x^2y^8cos^3(x^3y^8)sin(x^3y^8)

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(\partial)/(\partial x)(cos^4(x^3y^8))

\frac{\partial}{\partial x} (cos^{4} (x^{3} y^{8}))

- 12 x^{2} y^{8} cos^{3} (x^{3} y^{8}) sin (x^{3} y^{8})

Solution steps

\frac{\partial}{\partial x} (cos^{4} (x^{3} y^{8}))

Treat

y

as a constant

Apply the chain rule:

4 (cos (x^{3} y^{8}))^{3} \frac{\partial}{\partial x} (cos (x^{3} y^{8}))

= 4 (cos (x^{3} y^{8}))^{3} \frac{\partial}{\partial x} (cos (x^{3} y^{8}))

\frac{\partial}{\partial x} (cos (x^{3} y^{8})) = - sin (x^{3} y^{8}) \cdot 3 y^{8} x^{2}

= 4 (cos (x^{3} y^{8}))^{3} (- sin (x^{3} y^{8}) \cdot 3 y^{8} x^{2})

Simplify

= - 12 x^{2} y^{8} cos^{3} (x^{3} y^{8}) sin (x^{3} y^{8})

f (x) = arctan (x)

y = x^{4 c o s (x)}

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

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

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

What is (\partial)/(\partial x)(cos^4(x^3y^8)) ?
The answer to (\partial)/(\partial x)(cos^4(x^3y^8)) is -12x^2y^8cos^3(x^3y^8)sin(x^3y^8)