What is the derivative of (7^{10x+1}) ?

The derivative of (7^{10x+1}) is 10ln(7)*7^{10x+1}

What is the first derivative of (7^{10x+1}) ?

The first derivative of (7^{10x+1}) is 10ln(7)*7^{10x+1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} ((7)^{10 x + 1})

10 ln (7) \cdot 7^{10 x + 1}

Solution steps

\frac{d}{d x} ((7)^{10 x + 1})

Apply exponent rule:

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

7^{10 x + 1} = e^{(10 x + 1) l n (7)}

= \frac{d}{d x} (e^{(10 x + 1) l n (7)})

Apply the chain rule:

e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

= e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

\frac{d}{d x} ((10 x + 1) ln (7)) = 10 ln (7)

= e^{(10 x + 1) l n (7)} \cdot 10 ln (7)

e^{(10 x + 1) l n (7)} = 7^{10 x + 1}

= 10 ln (7) \cdot 7^{10 x + 1}

What is the derivative of (7^{10x+1}) ?
The derivative of (7^{10x+1}) is 10ln(7)*7^{10x+1}
What is the first derivative of (7^{10x+1}) ?
The first derivative of (7^{10x+1}) is 10ln(7)*7^{10x+1}