What is (\partial)/(\partial x)(2kx^2y^2-xsin(y)) ?

The answer to (\partial)/(\partial x)(2kx^2y^2-xsin(y)) is 4y^2kx-sin(y)

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(\partial)/(\partial x)(2kx^2y^2-xsin(y))

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

4 y^{2} k x - sin (y)

Solution steps

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

Treat

k, y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 k x^{2} y^{2}) - \frac{\partial}{\partial x} (x sin (y))

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

\frac{\partial}{\partial x} (x sin (y)) = sin (y)

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

\frac{2 e ^{- 2 s}}{s ^{2} - 4}

e^{t} - t

\int \frac{2}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

x \to 4 lim (0.1 x^{2} + 3 x + 2)

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

What is (\partial)/(\partial x)(2kx^2y^2-xsin(y)) ?
The answer to (\partial)/(\partial x)(2kx^2y^2-xsin(y)) is 4y^2kx-sin(y)