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

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

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

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

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

Solution steps

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

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^{2}))

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

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

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

n = 0 \sum \infty \frac{2}{3}

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

t an g e n t f (x) = \frac{1}{x}, at x = a

\int 10 w w d w

d er i v a t i v e f (x) = (x + 2) e^{\frac{1}{x}}

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