What is the derivative of-2(e^xsin(x+cos(x)e^x)) ?

The derivative of-2(e^xsin(x+cos(x)e^x)) is -4e^xcos(x)

What is the first derivative of-2(e^xsin(x+cos(x)e^x)) ?

The first derivative of-2(e^xsin(x+cos(x)e^x)) is -4e^xcos(x)

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\frac{d}{d x} (- 2 (e^{x} sin (x) + cos (x) e^{x}))

- 4 e^{x} cos (x)

Solution steps

\frac{d}{d x} (- 2 (e^{x} sin (x) + cos (x) e^{x}))

Take the constant out:

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

= - 2 \frac{d}{d x} (e^{x} sin (x) + cos (x) e^{x})

Apply the Sum/Difference Rule:

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

= - 2 (\frac{d}{d x} (e^{x} sin (x)) + \frac{d}{d x} (cos (x) e^{x}))

\frac{d}{d x} (e^{x} sin (x)) = e^{x} sin (x) + cos (x) e^{x}

\frac{d}{d x} (cos (x) e^{x}) = - e^{x} sin (x) + e^{x} cos (x)

= - 2 (e^{x} sin (x) + cos (x) e^{x} - e^{x} sin (x) + e^{x} cos (x))

Simplify

= - 4 e^{x} cos (x)

\int \frac{1}{5 + 2 x ^{4}} (8 x^{3}) d x

\frac{d}{d x} (8 sin (x) - 4 2 x)

{cos (t)}

f (t) = cos (8 t)

What is the derivative of-2(e^xsin(x+cos(x)e^x)) ?
The derivative of-2(e^xsin(x+cos(x)e^x)) is -4e^xcos(x)
What is the first derivative of-2(e^xsin(x+cos(x)e^x)) ?
The first derivative of-2(e^xsin(x+cos(x)e^x)) is -4e^xcos(x)