What is the derivative of 5^{3x}+7 ?

The derivative of 5^{3x}+7 is 3ln(5)*125^x

What is the first derivative of 5^{3x}+7 ?

The first derivative of 5^{3x}+7 is 3ln(5)*125^x

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\frac{d}{d x} (5^{3 x} + 7)

3 ln (5) \cdot 12 5^{x}

Solution steps

\frac{d}{d x} (5^{3 x} + 7)

Simplify

5^{3 x} + 7 : 12 5^{x} + 7

= \frac{d}{d x} (12 5^{x} + 7)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (12 5^{x}) + \frac{d}{d x} (7)

\frac{d}{d x} (12 5^{x}) = 3 ln (5) \cdot 12 5^{x}

\frac{d}{d x} (7) = 0

= 3 ln (5) \cdot 12 5^{x} + 0

Simplify

= 3 ln (5) \cdot 12 5^{x}

What is the derivative of 5^{3x}+7 ?
The derivative of 5^{3x}+7 is 3ln(5)*125^x
What is the first derivative of 5^{3x}+7 ?
The first derivative of 5^{3x}+7 is 3ln(5)*125^x