Question

EײIn2x with respect to x

Answer 1

`(dy)/(dx) = e^{x^(2) } ( (1)/(x) + 2x ln2x )</strong></p><p><strong>Step-by-step explanation:</strong></p><p>Let Given function<strong> (y) = [tex]e^{x^(2)} ln2x`

If we differentiate this function with respect to x -

`(dy)/(dx) = (d)/(dx) ( e^{x^(2) } ln2x)`

As we know that-

\frac{d}{dx} ( I × II ) = I × \frac{d}{dx} ( II ) + II × \frac{d}{dx} (I)

[tex]\frac{dy}{dx} = e^{x^{2} } \frac{d}{dx} ( ln2x ) + ln2x \frac{d}{dx} ( e^{x^{2} })

[tex]\frac{dy}{dx} = e^{x^{2} } \frac{1}{2x} × 2 + ln2x × e^{x^{2} } × 2x

[tex]\frac{dy}{dx} = e^{x^{2} } \frac{1}{x} + ln2x × e^{x^{2} } × 2x

[tex]\frac{dy}{dx} = e^{x^{2} } ( \frac{1}{x} + 2x ln2x )