What is (\partial)/(\partial x)((e^x-4x)sin(y)) ?

The answer to (\partial)/(\partial x)((e^x-4x)sin(y)) is sin(y)(e^x-4)

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(\partial)/(\partial x)((e^x-4x)sin(y))

\frac{\partial}{\partial x} ((e^{x} - 4 x) sin (y))

sin (y) (e^{x} - 4)

Solution steps

\frac{\partial}{\partial x} ((e^{x} - 4 x) sin (y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= sin (y) \frac{\partial}{\partial x} (e^{x} - 4 x)

Apply the Sum/Difference Rule:

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

= sin (y) (\frac{\partial}{\partial x} (e^{x}) - \frac{\partial}{\partial x} (4 x))

\frac{\partial}{\partial x} (e^{x}) = e^{x}

\frac{\partial}{\partial x} (4 x) = 4

= sin (y) (e^{x} - 4)

y = (x - 2) (x^{2} + 4), (1, - 5)

ln (2)

\frac{d y}{d x} = \frac{y}{x + 1} + 4 x^{2} + 4 x

\int_{\frac{4}{3}}^{4} \frac{1}{1 - x ^{2}} d x

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

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