What is the derivative of 5^{2x+6}(ln(5x+7)) ?

The derivative of 5^{2x+6}(ln(5x+7)) is 2ln(5)*5^{2x+6}ln(5x+7)+(5^{2x+7})/(5x+7)

What is the first derivative of 5^{2x+6}(ln(5x+7)) ?

The first derivative of 5^{2x+6}(ln(5x+7)) is 2ln(5)*5^{2x+6}ln(5x+7)+(5^{2x+7})/(5x+7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

5^{2 x + 6} (ln (5 x + 7))

2 ln (5) \cdot 5^{2 x + 6} ln (5 x + 7) + \frac{5 ^{2 x + 7}}{5 x + 7}

Solution steps

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

Apply the Product Rule:

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

f = 5^{2 x + 6}, g = ln (5 x + 7)

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

\frac{d}{d x} (5^{2 x + 6}) = 2 ln (5) \cdot 5^{2 x + 6}

\frac{d}{d x} (ln (5 x + 7)) = \frac{5}{5 x + 7}

= 2 ln (5) \cdot 5^{2 x + 6} ln (5 x + 7) + \frac{5}{5 x + 7} \cdot 5^{2 x + 6}

\frac{5}{5 x + 7} \cdot 5^{2 x + 6} = \frac{5 ^{2 x + 7}}{5 x + 7}

= 2 ln (5) \cdot 5^{2 x + 6} ln (5 x + 7) + \frac{5 ^{2 x + 7}}{5 x + 7}

\int 9 x^{2} - 1 d x

f (x) = 4 sec (x)

(ln (6 x))^{11}

x \to 5 - lim (\frac{x}{x + 1})

x \to 0 lim (- x)

What is the derivative of 5^{2x+6}(ln(5x+7)) ?
The derivative of 5^{2x+6}(ln(5x+7)) is 2ln(5)*5^{2x+6}ln(5x+7)+(5^{2x+7})/(5x+7)
What is the first derivative of 5^{2x+6}(ln(5x+7)) ?
The first derivative of 5^{2x+6}(ln(5x+7)) is 2ln(5)*5^{2x+6}ln(5x+7)+(5^{2x+7})/(5x+7)