What is (\partial)/(\partial x)(-2sin(2x)-2xe^{5y}) ?

The answer to (\partial)/(\partial x)(-2sin(2x)-2xe^{5y}) is -4cos(2x)-2e^{5y}

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(\partial)/(\partial x)(-2sin(2x)-2xe^{5y})

\frac{\partial}{\partial x} (- 2 sin (2 x) - 2 x e^{5 y})

- 4 cos (2 x) - 2 e^{5 y}

Solution steps

\frac{\partial}{\partial x} (- 2 sin (2 x) - 2 x e^{5 y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial x} (2 sin (2 x)) - \frac{\partial}{\partial x} (2 x e^{5 y})

\frac{\partial}{\partial x} (2 sin (2 x)) = 4 cos (2 x)

\frac{\partial}{\partial x} (2 x e^{5 y}) = 2 e^{5 y}

= - 4 cos (2 x) - 2 e^{5 y}

f (s) = \frac{s}{s ^{2} + 1}

\int_{- 1}^{0} \frac{3}{3 x - 2} d x

f (x) = - 3 x^{2} + 6 x + 4

\frac{d}{d x} ((1 + 2 x)^{l n (x)})

h \to 0 lim (\frac{0}{h})

What is (\partial)/(\partial x)(-2sin(2x)-2xe^{5y}) ?
The answer to (\partial)/(\partial x)(-2sin(2x)-2xe^{5y}) is -4cos(2x)-2e^{5y}