What is (\partial)/(\partial x)(cos^6(x^2y^9)) ?

The answer to (\partial)/(\partial x)(cos^6(x^2y^9)) is -12xy^9cos^5(x^2y^9)sin(x^2y^9)

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(\partial)/(\partial x)(cos^6(x^2y^9))

\frac{\partial}{\partial x} (cos^{6} (x^{2} y^{9}))

- 12 x y^{9} cos^{5} (x^{2} y^{9}) sin (x^{2} y^{9})

Solution steps

\frac{\partial}{\partial x} (cos^{6} (x^{2} y^{9}))

Treat

y

as a constant

Apply the chain rule:

6 (cos (x^{2} y^{9}))^{5} \frac{\partial}{\partial x} (cos (x^{2} y^{9}))

= 6 (cos (x^{2} y^{9}))^{5} \frac{\partial}{\partial x} (cos (x^{2} y^{9}))

\frac{\partial}{\partial x} (cos (x^{2} y^{9})) = - sin (x^{2} y^{9}) \cdot 2 y^{9} x

= 6 (cos (x^{2} y^{9}))^{5} (- sin (x^{2} y^{9}) \cdot 2 y^{9} x)

Simplify

= - 12 x y^{9} cos^{5} (x^{2} y^{9}) sin (x^{2} y^{9})

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

cos (x), \frac{π}{2}

\frac{\partial}{\partial y} (x^{4} y - 3 x^{5} y^{2})

x \to 1 lim (x + 1)

\int x ln (3 x) d x

What is (\partial)/(\partial x)(cos^6(x^2y^9)) ?
The answer to (\partial)/(\partial x)(cos^6(x^2y^9)) is -12xy^9cos^5(x^2y^9)sin(x^2y^9)