What is the derivative of (sqrt(3)^x) ?

The derivative of (sqrt(3)^x) is 1/2 ln(3)e^{(ln(3)x)/2}

What is the first derivative of (sqrt(3)^x) ?

The first derivative of (sqrt(3)^x) is 1/2 ln(3)e^{(ln(3)x)/2}

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

\frac{1}{2} ln (3) e^{\frac{l n ( 3 ) x}{2}}

Solution steps

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

Simplify

(3)^{x} : 3^{\frac{x}{2}}

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2} ln (3)) = \frac{1}{2} ln (3)

= e^{\frac{x}{2} l n (3)} \frac{1}{2} ln (3)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1}{2} ln (3) e^{\frac{l n ( 3 ) x}{2}}

\int \frac{2 x + 1}{4 x ^{2} + 4 x + 7} d x

f (x) = 3 sin (x)

F (r) = \frac{2}{r ^{3}}

\frac{\partial}{\partial x} (\frac{6}{5} - \frac{6}{5} e^{- 20 t})

\frac{d}{d t} (2 cos (3 t))

What is the derivative of (sqrt(3)^x) ?
The derivative of (sqrt(3)^x) is 1/2 ln(3)e^{(ln(3)x)/2}
What is the first derivative of (sqrt(3)^x) ?
The first derivative of (sqrt(3)^x) is 1/2 ln(3)e^{(ln(3)x)/2}