What is the derivative of 5^{x-1} ?

The derivative of 5^{x-1} is ln(5)*5^{x-1}

What is the first derivative of 5^{x-1} ?

The first derivative of 5^{x-1} is ln(5)*5^{x-1}

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\frac{d}{d x} (5^{x - 1})

ln (5) \cdot 5^{x - 1}

Solution steps

\frac{d}{d x} (5^{x - 1})

Apply exponent rule:

a^{b} = e^{b l n (a)}

5^{x - 1} = e^{(x - 1) l n (5)}

= \frac{d}{d x} (e^{(x - 1) l n (5)})

Apply the chain rule:

e^{(x - 1) l n (5)} \frac{d}{d x} ((x - 1) ln (5))

= e^{(x - 1) l n (5)} \frac{d}{d x} ((x - 1) ln (5))

\frac{d}{d x} ((x - 1) ln (5)) = ln (5)

= e^{(x - 1) l n (5)} ln (5)

e^{(x - 1) l n (5)} = 5^{x - 1}

= ln (5) \cdot 5^{x - 1}

G (t) = \frac{4 t}{t + 1}

f (x) = x^{2} + 5 x, at x = 4

\int x e^{- x} - e^{- x} d x

\frac{\partial}{\partial x} (3 e^{3 x})

y^{^{'}} = y (1 - y), y (0) = 8

What is the derivative of 5^{x-1} ?
The derivative of 5^{x-1} is ln(5)*5^{x-1}
What is the first derivative of 5^{x-1} ?
The first derivative of 5^{x-1} is ln(5)*5^{x-1}