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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derivative of

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)

x \to - 1 lim (\frac{1}{x ^{3} - x})

y^{8} - \frac{y ^{9} + 4}{x ^{3} 4 y ^{^{'}}} = 0

\int (- x x^{4}) d x

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

\frac{\partial}{\partial t} (\frac{( s - 2 r )}{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)