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

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

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

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

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

Solution steps

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

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

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

= 4 y x - sin (x^{2}) \cdot 2 x

\frac{t ^{2} - 1}{t ^{2} + t - 2}

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

\int 10 x d x

f (x) = - 3 e^{x^{2} + x - 1}

x^{2} y^{^{'}} + 2 x y = ln (x), y (1) = 7

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