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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

y^{^{'}} + 5 y = 1

(- 3, 2), (5, - 4)

x \to - 1 lim (x^{2} + x + 1)

\frac{d}{d x} (\frac{x ^{2}}{( 1 + x )})

\frac{d}{d t} (e^{3 t})

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