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

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

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

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

- 12 x^{3} y^{3} cos^{2} (x^{4} y^{3}) sin (x^{4} y^{3})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

= 3 (cos (x^{4} y^{3}))^{2} \frac{\partial}{\partial x} (cos (x^{4} y^{3}))

\frac{\partial}{\partial x} (cos (x^{4} y^{3})) = - sin (x^{4} y^{3}) \cdot 4 y^{3} x^{3}

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

Simplify

= - 12 x^{3} y^{3} cos^{2} (x^{4} y^{3}) sin (x^{4} y^{3})

y^{^{''}} + 9 y = 27

x \to 2 + lim (x^{2} - 4)

\frac{d}{d x} (\frac{8}{cos ( x ^{2} - 2 x )})

x cos (x) + 2 tan (x)

\int_{5}^{7} \frac{x}{x ^{2} + 6 x + 13} d x

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