What is the derivative of (x+2^{2x-3}) ?

The derivative of (x+2^{2x-3}) is (2ln(x+2)+(2x-3)/(x+2))(x+2)^{2x-3}

What is the first derivative of (x+2^{2x-3}) ?

The first derivative of (x+2^{2x-3}) is (2ln(x+2)+(2x-3)/(x+2))(x+2)^{2x-3}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

(2 ln (x + 2) + \frac{2 x - 3}{x + 2}) (x + 2)^{2 x - 3}

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

(x + 2)^{2 x - 3} = e^{(2 x - 3) l n (x + 2)}

= \frac{d}{d x} (e^{(2 x - 3) l n (x + 2)})

Apply the chain rule:

e^{(2 x - 3) l n (x + 2)} \frac{d}{d x} ((2 x - 3) ln (x + 2))

= e^{(2 x - 3) l n (x + 2)} \frac{d}{d x} ((2 x - 3) ln (x + 2))

\frac{d}{d x} ((2 x - 3) ln (x + 2)) = 2 ln (x + 2) + \frac{2 x - 3}{x + 2}

= e^{(2 x - 3) l n (x + 2)} (2 ln (x + 2) + \frac{2 x - 3}{x + 2})

e^{(2 x - 3) l n (x + 2)} = (x + 2)^{2 x - 3}

= (2 ln (x + 2) + \frac{2 x - 3}{x + 2}) (x + 2)^{2 x - 3}

\frac{d}{d t} (e^{- i t})

x \to 6 lim (c x^{2} + 9 x)

\frac{\partial}{\partial u} (\frac{v - u}{2})

(- 3, - 8), (5, 6)

\frac{\partial}{\partial x} (x^{2} y + 2 y^{2} - 6 x + 3 y - 4)

What is the derivative of (x+2^{2x-3}) ?
The derivative of (x+2^{2x-3}) is (2ln(x+2)+(2x-3)/(x+2))(x+2)^{2x-3}
What is the first derivative of (x+2^{2x-3}) ?
The first derivative of (x+2^{2x-3}) is (2ln(x+2)+(2x-3)/(x+2))(x+2)^{2x-3}