What is the derivative of f(x)=6e^x(cos(x)-sin(x)) ?

The derivative of f(x)=6e^x(cos(x)-sin(x)) is -12e^xsin(x)

What is the first derivative of f(x)=6e^x(cos(x)-sin(x)) ?

The first derivative of f(x)=6e^x(cos(x)-sin(x)) is -12e^xsin(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

- 12 e^{x} sin (x)

Solution steps

\frac{d}{d x} (6 e^{x} (cos (x) - sin (x)))

Take the constant out:

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

= 6 \frac{d}{d x} (e^{x} (cos (x) - sin (x)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (x) - sin (x)

= 6 (\frac{d}{d x} (e^{x}) (cos (x) - sin (x)) + \frac{d}{d x} (cos (x) - sin (x)) e^{x})

\frac{d}{d x} (e^{x}) = e^{x}

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

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

Simplify

6 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x}) : - 12 e^{x} sin (x)

= - 12 e^{x} sin (x)

3 t^{7} + 4 t^{5} - t

\frac{d}{d x} (ln (\frac{4 x ^{2} - 9}{2 x - 3}))

x \to 1 + lim (x^{2} - x)

\frac{\partial}{\partial y} (x^{3} - 3 x y + y^{3})

x^{2} sin^{3} (x) + x cos^{- 3} (x)

What is the derivative of f(x)=6e^x(cos(x)-sin(x)) ?
The derivative of f(x)=6e^x(cos(x)-sin(x)) is -12e^xsin(x)
What is the first derivative of f(x)=6e^x(cos(x)-sin(x)) ?
The first derivative of f(x)=6e^x(cos(x)-sin(x)) is -12e^xsin(x)