What is the derivative of g(x)=3^{(x/2)} ?

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

What is the first derivative of g(x)=3^{(x/2)} ?

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

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derivative of

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

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

Solution steps

\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 2 lim (\frac{( 3 )}{x - 2})

\int sec^{7} (3 x) tan (3 x) d x

x \to 0 - lim (cot (x))

(x (csc (\frac{y}{x})) - y) d x + x d y = 0

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

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