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Popular >

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

Solution

derivative of

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

Solution

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)

Popular Examples

(dy)/(dx)=(e^{3x+2y})

\frac{d y}{d x} = (e^{3 x + 2 y})

integral from-3 to 3 of 1/(1+x^2)

\int_{- 3}^{3} \frac{1}{1 + x ^{2}} d x

(dy)/(dx)=x^8y^{-7}

\frac{d y}{d x} = x^{8} y^{- 7}

t*(dy)/(dt)=t^3+9t^3y

t \cdot \frac{d y}{d t} = t^{3} + 9 t^{3} y

derivative of (x^2+x^2sin^3(2x))

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

Frequently Asked Questions (FAQ)

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)