What is (\partial)/(\partial x)(cos^3(x^7y^3)) ?

The answer to (\partial)/(\partial x)(cos^3(x^7y^3)) is -21x^6y^3cos^2(x^7y^3)sin(x^7y^3)

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(\partial)/(\partial x)(cos^3(x^7y^3))

\frac{\partial}{\partial x} (cos^{3} (x^{7} y^{3}))

- 21 x^{6} y^{3} cos^{2} (x^{7} y^{3}) sin (x^{7} y^{3})

Solution steps

\frac{\partial}{\partial x} (cos^{3} (x^{7} y^{3}))

Treat

y

as a constant

Apply the chain rule:

3 (cos (x^{7} y^{3}))^{2} \frac{\partial}{\partial x} (cos (x^{7} y^{3}))

= 3 (cos (x^{7} y^{3}))^{2} \frac{\partial}{\partial x} (cos (x^{7} y^{3}))

\frac{\partial}{\partial x} (cos (x^{7} y^{3})) = - sin (x^{7} y^{3}) \cdot 7 y^{3} x^{6}

= 3 (cos (x^{7} y^{3}))^{2} (- sin (x^{7} y^{3}) \cdot 7 y^{3} x^{6})

Simplify

= - 21 x^{6} y^{3} cos^{2} (x^{7} y^{3}) sin (x^{7} y^{3})

\frac{\partial}{\partial x} (9 x^{2} y - 3 x^{5} y)

\frac{\partial}{\partial x} (x \cdot y \cdot z)

x \to 4 + lim (\frac{( 7 x )}{x - 4})

\int \frac{8}{4 x ^{2} + 1} d x

y = 1 - x^{2}, y = 29 - 11 x

What is (\partial)/(\partial x)(cos^3(x^7y^3)) ?
The answer to (\partial)/(\partial x)(cos^3(x^7y^3)) is -21x^6y^3cos^2(x^7y^3)sin(x^7y^3)