What is the derivative of 8(e^xcos(x-e^xsin(x))) ?

The derivative of 8(e^xcos(x-e^xsin(x))) is -16e^xsin(x)

What is the first derivative of 8(e^xcos(x-e^xsin(x))) ?

The first derivative of 8(e^xcos(x-e^xsin(x))) is -16e^xsin(x)

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\frac{d}{d x} (8 (e^{x} cos (x) - e^{x} sin (x)))

- 16 e^{x} sin (x)

Solution steps

\frac{d}{d x} (8 (e^{x} cos (x) - e^{x} sin (x)))

Take the constant out:

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

= 8 \frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

Apply the Sum/Difference Rule:

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

= 8 (\frac{d}{d x} (e^{x} cos (x)) - \frac{d}{d x} (e^{x} sin (x)))

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

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

= 8 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x}))

Simplify

8 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x})) : - 16 e^{x} sin (x)

= - 16 e^{x} sin (x)

\int \frac{x ^{4} - 5 x ^{3} + 5 x ^{2} + 8}{x ^{3} + 3 x ^{2}} d x

f (x) = 5 x^{2} (x^{3} + 2)

\frac{d}{d x} (3 x^{3 x})

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

\int \frac{t}{( 3 t ^{2} + 1 ) ^{4}} d t

What is the derivative of 8(e^xcos(x-e^xsin(x))) ?
The derivative of 8(e^xcos(x-e^xsin(x))) is -16e^xsin(x)
What is the first derivative of 8(e^xcos(x-e^xsin(x))) ?
The first derivative of 8(e^xcos(x-e^xsin(x))) is -16e^xsin(x)