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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

\int - \frac{1}{4 - x} d x

(x^{2} + 4) sin (5 x)

θ \to 0 + lim (\frac{s}{d})

x \to 1 + lim (x^{\frac{5}{1 - x}})

(y + 1) d x = 2 x y d y

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