Question

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Answer 1

$\frac{d(lnx)}{dx}=\frac{1}{x}$

Answer:

$\frac{dy}{dx}=e^{x^2}(\frac{2x^2ln(4x^3)+3}{x})$

Step-by-step explanation:

We are given that a function

$y=e^{x^2}ln(4x^3)$

We have to differentiate w.r.t x

$\frac{dy}{dx}=e^{x^2}\times 2xln(4x^3)+e^{x^2}\times \frac{1}{4x^3}\times 12x^2$

By using formula

$\frac{d(lnx)}{dx}=\frac{1}{x}$

$\frac{d(e^x)}{dx}=e^x$

$\frac{dy}{dx}=e^{x^2}(2xln(4x^3)+\frac{3}{x})$

$\frac{dy}{dx}=e^{x^2}(\frac{2x^2ln(4x^3)+3}{x})$

Hence, the derivative of function

$\frac{dy}{dx}=e^{x^2}(\frac{2x^2ln(4x^3)+3}{x})$