What is the derivative of (3/2 ^xln(3/2)) ?

The derivative of (3/2 ^xln(3/2)) is ln^2(3/2)(3/2)^x

What is the first derivative of (3/2 ^xln(3/2)) ?

The first derivative of (3/2 ^xln(3/2)) is ln^2(3/2)(3/2)^x

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

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

Simplify

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

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

\int x^{3} 2 + x^{4} d x

\frac{\partial}{\partial y} (x^{2} + 3 x - 4 x y)

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

\int - \frac{1}{t} d t

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

What is the derivative of (3/2 ^xln(3/2)) ?
The derivative of (3/2 ^xln(3/2)) is ln^2(3/2)(3/2)^x
What is the first derivative of (3/2 ^xln(3/2)) ?
The first derivative of (3/2 ^xln(3/2)) is ln^2(3/2)(3/2)^x