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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derivative of

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}}

x \to \infty lim (5^{x} + 1)

x^{2}, 6 - x

\frac{1}{1 - x ^{3}}

e^{a \cdot t}

f (x) = x e^{x}

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}