What is the derivative of (a^x/(ln(a))) ?

The derivative of (a^x/(ln(a))) is a^x

What is the first derivative of (a^x/(ln(a))) ?

The first derivative of (a^x/(ln(a))) is a^x

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

a^{x}

Solution steps

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

Take the constant out:

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

= \frac{1}{ln ( a )} \frac{d}{d x} (a^{x})

Apply the derivative exponent rule:

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

= \frac{1}{ln ( a )} a^{x} ln (a)

Simplify

\frac{1}{ln ( a )} a^{x} ln (a) : a^{x}

= a^{x}

\frac{d}{d x} (\frac{e ^{x}}{( 1 + e ^{2 x} ) ^{\frac{3}{2}}})

\int \frac{( x ^{2} - a ^{2} ) ^{\frac{3}{2}}}{x} d x

\frac{d y}{d t} = \frac{y}{t + 1} + 4 t^{2} + 4 t, y (1) = 12

y = 5 x^{8} - 3 x^{5} + 2, (0, 4)

\frac{d}{d x} (θ (x)), tan (θ (x)) = \frac{x}{35}

What is the derivative of (a^x/(ln(a))) ?
The derivative of (a^x/(ln(a))) is a^x
What is the first derivative of (a^x/(ln(a))) ?
The first derivative of (a^x/(ln(a))) is a^x