derivative of 5^t — step-by-step solution

Let's perform the differentiation:

\frac{d}{d t} (5^{t})

You can rewrite the expression:

5^{t}

as:

e^{t \cdot \ln (5)}

ⅰ

\frac{d}{d t} (5^{t})

\frac{d}{d t} (t \cdot \ln (5)) \cdot e^{t \cdot \ln (5)}

\frac{d}{d t} (t \cdot \ln (5)) \cdot e^{t \cdot \ln (5)}

ⓘ A constant factor stays in front of the derivative, (k*u)' = k*u':

\frac{d}{d t} (t \cdot \ln (5))

\ln (5)

■As exp and ln are inverse of each other, exp(n*ln(x)) = x^n:

e^{t \cdot \ln (5)}

5^{t}

\ln (5) \cdot 5^{t}

▶Derivative:

5^{t} \cdot \ln (5)