What is the derivative of 4(e^xcos(x-e^xsin(x))) ?

The derivative of 4(e^xcos(x-e^xsin(x))) is -8e^xsin(x)

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

The first derivative of 4(e^xcos(x-e^xsin(x))) is -8e^xsin(x)

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Popular >

\frac{d}{d x} (4 (e^{x} cos (x) - e^{x} sin (x)))

- 8 e^{x} sin (x)

Solution steps

\frac{d}{d x} (4 (e^{x} cos (x) - e^{x} sin (x)))

Take the constant out:

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

= 4 \frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

Apply the Sum/Difference Rule:

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

= 4 (\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}

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

Simplify

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

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

\int \frac{x ^{2}}{( 9 - x ^{3} ) ^{2}} d x

\int e^{3 x} d x

\int_{0}^{5} 1 + x^{2} d x

\frac{d}{d n} (cos (n m^{3}))

\frac{d}{d x} (3 x^{2} - x^{3})

What is the derivative of 4(e^xcos(x-e^xsin(x))) ?
The derivative of 4(e^xcos(x-e^xsin(x))) is -8e^xsin(x)
What is the first derivative of 4(e^xcos(x-e^xsin(x))) ?
The first derivative of 4(e^xcos(x-e^xsin(x))) is -8e^xsin(x)