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

The answer to (\partial)/(\partial x)(2x^2y+sin(x^3)) is 4yx+cos(x^3)*3x^2

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (2 x^{2} y) = 4 y x

\frac{\partial}{\partial x} (sin (x^{3})) = cos (x^{3}) \cdot 3 x^{2}

= 4 y x + cos (x^{3}) \cdot 3 x^{2}

y = 4 e^{x} + x, (0, 4)

\int_{- π}^{π} x \cdot sin (n \cdot x) d x

\int - sin (x) sec (x) tan (x) d x

\int 4 x^{3} - \frac{3}{x ^{4}} d x

3 - 9 x

What is (\partial)/(\partial x)(2x^2y+sin(x^3)) ?
The answer to (\partial)/(\partial x)(2x^2y+sin(x^3)) is 4yx+cos(x^3)*3x^2