What is (\partial)/(\partial x)(cos(x^2+y^3)) ?

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

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(\partial)/(\partial x)(cos(x^2+y^3))

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

- sin (x^{2} + y^{3}) \cdot 2 x

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

- sin (x^{2} + y^{3}) \frac{\partial}{\partial x} (x^{2} + y^{3})

= - sin (x^{2} + y^{3}) \frac{\partial}{\partial x} (x^{2} + y^{3})

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

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

x \to π lim (\frac{1}{cos ( x )})

f (x) = \frac{x}{x ^{2} + 11}

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

x \to - \infty lim (4^{x} + 5)

\int_{1}^{4} \frac{1}{4 x + 7} d x

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