What is the derivative of 3^{x/2} ?

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

What is the first derivative of 3^{x/2} ?

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

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\frac{d}{d 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}}

\frac{d}{d x} (x^{3} + x^{2} - 5 x)

\int x \cdot e^{5 x} d x

\int (\frac{1}{x ^{2}} - 1) d x

x \to 0 lim (\frac{5 sin ( x )}{x})

\int (x - 1)^{2} (x - 2) (x - 4) d x

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