What is the derivative of e^{3x^2}+ln(5x-4) ?

The derivative of e^{3x^2}+ln(5x-4) is e^{3x^2}*6x+5/(5x-4)

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

The first derivative of e^{3x^2}+ln(5x-4) is e^{3x^2}*6x+5/(5x-4)

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

e^{3 x^{2}} \cdot 6 x + \frac{5}{5 x - 4}

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{3 x^{2}}) + \frac{d}{d x} (ln (5 x - 4))

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

\frac{d}{d x} (ln (5 x - 4)) = \frac{5}{5 x - 4}

= e^{3 x^{2}} \cdot 6 x + \frac{5}{5 x - 4}

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