What is the derivative of y=5sqrt(7e^{-2x)+6} ?

The derivative of y=5sqrt(7e^{-2x)+6} is -(35e^{-2x})/(sqrt(7e^{-2x)+6)}

What is the first derivative of y=5sqrt(7e^{-2x)+6} ?

The first derivative of y=5sqrt(7e^{-2x)+6} is -(35e^{-2x})/(sqrt(7e^{-2x)+6)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = 5 7 e^{- 2 x} + 6

- \frac{35 e ^{- 2 x}}{7 e ^{- 2 x} + 6}

Solution steps

\frac{d}{d x} (5 7 e^{- 2 x} + 6)

Take the constant out:

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

= 5 \frac{d}{d x} (7 e^{- 2 x} + 6)

Apply the chain rule:

\frac{1}{2 7 e ^{- 2 x} + 6} \frac{d}{d x} (7 e^{- 2 x} + 6)

= \frac{1}{2 7 e ^{- 2 x} + 6} \frac{d}{d x} (7 e^{- 2 x} + 6)

\frac{d}{d x} (7 e^{- 2 x} + 6) = - 14 e^{- 2 x}

= 5 \cdot \frac{1}{2 7 e ^{- 2 x} + 6} (- 14 e^{- 2 x})

Simplify

5 \cdot \frac{1}{2 7 e ^{- 2 x} + 6} (- 14 e^{- 2 x}) : - \frac{35 e ^{- 2 x}}{7 e ^{- 2 x} + 6}

= - \frac{35 e ^{- 2 x}}{7 e ^{- 2 x} + 6}

x \to 0 lim (2 x - 4)

y = - 5 x^{2}

\frac{d}{d x} ((x^{2} + 9)^{5})

y = \frac{2 x}{e ^{x}}

\frac{d y}{d t} = \frac{( 4 y ^{2} - t ^{2} )}{2 t y}

What is the derivative of y=5sqrt(7e^{-2x)+6} ?
The derivative of y=5sqrt(7e^{-2x)+6} is -(35e^{-2x})/(sqrt(7e^{-2x)+6)}
What is the first derivative of y=5sqrt(7e^{-2x)+6} ?
The first derivative of y=5sqrt(7e^{-2x)+6} is -(35e^{-2x})/(sqrt(7e^{-2x)+6)}