$\dfrac d{dx}3^{x}=3^x \log(3)?$

Calculus Level 2

$\large\dfrac{d}{dx}{3}^{{x}^{{2}}}=?$

{3}^{{x}^{{2}}} x\log(9)

3^{x} \log(3)

{9}^{{x}^{{2}}} x\log(6)

{3}^{{2x}^{{2}}} x\log(3)

1 solution

Chew-Seong Cheong
Nov 11, 2017

$\large \frac d{dx} 3^{x^2} = \frac d{dx} e^{x^2\ln 3} = 2x\ln 3 \cdot e^{x^2\ln 3} = \boxed{3^{x^2} x\ln 9}$

@Chew-Seong Cheong in the title: how ' $d 3^{x^2}/dx=3^x \log(3)$ ?'

Nazmus sakib - 3 years, 6 months ago

I find the other one ugly and changed it. Shouldn't the question as title.

Chew-Seong Cheong - 3 years, 6 months ago

but it is still how $\dfrac {d 3^{x^2}}{dx}=3^x \log(3)$ ? should it be $\dfrac {d 3^{x}}{dx}=3^x \log(3)$ ?

Nazmus sakib - 3 years, 6 months ago

@Nazmus Sakib – I thought it was what you put.

Chew-Seong Cheong - 3 years, 6 months ago

@Chew-Seong Cheong – No.I gave the title a name like : $\dfrac d{dx}3^{x}=3^x \log(3)$ .

Nazmus sakib - 3 years, 6 months ago