What is the derivative of f(x)=6^{2x}+3^x ?

The derivative of f(x)=6^{2x}+3^x is ln(6)*9^x*2^{2x+1}+3^xln(3)

What is the first derivative of f(x)=6^{2x}+3^x ?

The first derivative of f(x)=6^{2x}+3^x is ln(6)*9^x*2^{2x+1}+3^xln(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = 6^{2 x} + 3^{x}

ln (6) \cdot 9^{x} \cdot 2^{2 x + 1} + 3^{x} ln (3)

Solution steps

\frac{d}{d x} (6^{2 x} + 3^{x})

Simplify

6^{2 x} + 3^{x} : 3 6^{x} + 3^{x}

= \frac{d}{d x} (3 6^{x} + 3^{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 6^{x}) + \frac{d}{d x} (3^{x})

\frac{d}{d x} (3 6^{x}) = ln (6) \cdot 9^{x} \cdot 2^{2 x + 1}

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

= ln (6) \cdot 9^{x} \cdot 2^{2 x + 1} + 3^{x} ln (3)

What is the derivative of f(x)=6^{2x}+3^x ?
The derivative of f(x)=6^{2x}+3^x is ln(6)*9^x*2^{2x+1}+3^xln(3)
What is the first derivative of f(x)=6^{2x}+3^x ?
The first derivative of f(x)=6^{2x}+3^x is ln(6)*9^x*2^{2x+1}+3^xln(3)