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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{d}{d x} (0.4 x^{2})

f (x) = \frac{x ^{2}}{2 ^{x}}

\frac{\partial}{\partial x} (x^{2} y + y)

f (x) = - 3 x^{3} + 2 x^{2} - 4 x + 7

\frac{d}{d x} (2.873 sec (x))

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