What is (\partial)/(\partial x)(cos(x^6-7y)) ?

The answer to (\partial)/(\partial x)(cos(x^6-7y)) is -sin(x^6-7y)*6x^5

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(\partial)/(\partial x)(cos(x^6-7y))

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

- sin (x^{6} - 7 y) \cdot 6 x^{5}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{6} - 7 y) = 6 x^{5}

= - sin (x^{6} - 7 y) \cdot 6 x^{5}

\int_{0}^{1} \frac{7}{x ( 1 + x )} d x

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

x \to 0 lim ((x^{2}) cos (\frac{8}{x}))

\frac{\partial}{\partial x} (- 10 x y sin (x y^{2}))

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

What is (\partial)/(\partial x)(cos(x^6-7y)) ?
The answer to (\partial)/(\partial x)(cos(x^6-7y)) is -sin(x^6-7y)*6x^5