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Popular >

derivative of ln(e^{3x^2}*4^{5x})

Solution

\frac{d}{d x} (ln (e^{3 x^{2}} \cdot 4^{5 x}))

Solution

10 ln (2) + 6 x

Solution steps

\frac{d}{d x} (ln (e^{3 x^{2}} \cdot 4^{5 x}))

Simplify

ln (e^{3 x^{2}} \cdot 4^{5 x}) : 10 ln (2) x + 3 x^{2}

= \frac{d}{d x} (10 ln (2) x + 3 x^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (10 ln (2) x) + \frac{d}{d x} (3 x^{2})

\frac{d}{d x} (10 ln (2) x) = 10 ln (2)

\frac{d}{d x} (3 x^{2}) = 6 x

= 10 ln (2) + 6 x

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(e^{3x^2}*4^{5x}) ?
The derivative of ln(e^{3x^2}*4^{5x}) is 10ln(2)+6x
What is the first derivative of ln(e^{3x^2}*4^{5x}) ?
The first derivative of ln(e^{3x^2}*4^{5x}) is 10ln(2)+6x