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

The answer to (\partial)/(\partial x)(cos^3(x^8y^8)) is -24x^7y^8cos^2(x^8y^8)sin(x^8y^8)

Popular >

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

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

- 24 x^{7} y^{8} cos^{2} (x^{8} y^{8}) sin (x^{8} y^{8})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

3 (cos (x^{8} y^{8}))^{2} \frac{\partial}{\partial x} (cos (x^{8} y^{8}))

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

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

= 3 (cos (x^{8} y^{8}))^{2} (- sin (x^{8} y^{8}) \cdot 8 y^{8} x^{7})

Simplify

= - 24 x^{7} y^{8} cos^{2} (x^{8} y^{8}) sin (x^{8} y^{8})

\frac{d}{d x} (\frac{1}{x \cdot ln ( x )})

x \to - 2 + lim (- 6)

f, tan (f) (x) = \frac{x + 1}{x ^{3}}

3 x^{2} + x y + 3 y^{2} = 7

\int cos (2 x + y) d x

What is (\partial)/(\partial x)(cos^3(x^8y^8)) ?
The answer to (\partial)/(\partial x)(cos^3(x^8y^8)) is -24x^7y^8cos^2(x^8y^8)sin(x^8y^8)