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Popular >

derivative of f(x)=5^{5x+1}+3^{1-3x}

Solution

derivative of

f (x) = 5^{5 x + 1} + 3^{1 - 3 x}

Solution

ln (5) \cdot 5^{5 x + 2} - ln (3) \cdot 3^{- 3 x + 2}

Solution steps

\frac{d}{d x} (5^{5 x + 1} + 3^{1 - 3 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5^{5 x + 1}) + \frac{d}{d x} (3^{1 - 3 x})

\frac{d}{d x} (5^{5 x + 1}) = ln (5) \cdot 5^{5 x + 2}

\frac{d}{d x} (3^{1 - 3 x}) = - ln (3) \cdot 3^{- 3 x + 2}

= ln (5) \cdot 5^{5 x + 2} - ln (3) \cdot 3^{- 3 x + 2}

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=5^{5x+1}+3^{1-3x} ?
The derivative of f(x)=5^{5x+1}+3^{1-3x} is ln(5)*5^{5x+2}-ln(3)*3^{-3x+2}
What is the first derivative of f(x)=5^{5x+1}+3^{1-3x} ?
The first derivative of f(x)=5^{5x+1}+3^{1-3x} is ln(5)*5^{5x+2}-ln(3)*3^{-3x+2}