What is the derivative of 3(e^xcos(x-e^xsin(x))) ?

The derivative of 3(e^xcos(x-e^xsin(x))) is -6e^xsin(x)

What is the first derivative of 3(e^xcos(x-e^xsin(x))) ?

The first derivative of 3(e^xcos(x-e^xsin(x))) is -6e^xsin(x)

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\frac{d}{d x} (3 (e^{x} cos (x) - e^{x} sin (x)))

- 6 e^{x} sin (x)

Solution steps

\frac{d}{d x} (3 (e^{x} cos (x) - e^{x} sin (x)))

Take the constant out:

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

= 3 \frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

Apply the Sum/Difference Rule:

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

= 3 (\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}

= 3 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x}))

Simplify

3 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x})) : - 6 e^{x} sin (x)

= - 6 e^{x} sin (x)

x \to 2 + lim (\frac{∣ x - 2 ∣}{x})

x \frac{d y}{d x} + 2 y = 3

\int_{- 3}^{- 3} 6 d x

\frac{d}{d x} ((7 + \frac{5}{x})^{x})

y = \frac{3 ( 2 x ^{5} - 7 )}{x ^{4}}

What is the derivative of 3(e^xcos(x-e^xsin(x))) ?
The derivative of 3(e^xcos(x-e^xsin(x))) is -6e^xsin(x)
What is the first derivative of 3(e^xcos(x-e^xsin(x))) ?
The first derivative of 3(e^xcos(x-e^xsin(x))) is -6e^xsin(x)