If y = 2x^{3x},then frac{dy}{dx} at x = 1 is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $y = 2x^{3x}$.Taking natural logarithm on both sides: $\ln y = \ln(2x^{3x}) = \ln 2 + 3x \ln x$.Differentiating both sides with respect to $

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(B) Given $y = 2x^{3x}$.Taking natural logarithm on both sides: $\ln y = \ln(2x^{3x}) = \ln 2 + 3x \ln x$.Differentiating both sides with respect to $x$: $\frac{1}{y} \frac{dy}{dx} = 0 + 3 \ln x + 3x \cdot \frac{1}{x} = 3 \ln x + 3$.Thus,$\frac{dy}{dx} = y(3 \ln x + 3) = 2x^{3x}(3 \ln x + 3)$.At $x = 1$,$\frac{dy}{dx} = 2(1)^{3(1)}(3 \ln 1 + 3)$.Since $\ln 1 = 0$,we have $\frac{dy}{dx} = 2(1)(0 + 3) = 2 	imes 3 = 6$.

If $y = 2x^{3x}$,then $\frac{dy}{dx}$ at $x = 1$ is

Similar Questions

If $y = \left(\frac{x^{2}}{x+1}\right)^{x}$ and $\frac{dy}{dx} = y \left[g(x) + \log \left(\frac{x^{2}}{x+1}\right)\right]$,then $g(x) =$

If ${x^m}{y^n} = 2{(x + y)^{m + n}},$ the value of $\frac{dy}{dx}$ is

Find $\frac{dy}{dx}$ for the function $(\cos x)^{y}=(\cos y)^{x}$.

If $y=x^{\sin x}+(\sin x)^x$,then $\frac{d y}{d x}$ at $x=\frac{\pi}{2}$ is

If $y = \log \left[e^{5x} \left(\frac{3x-4}{x+5}\right)^{\frac{4}{3}}\right]$,then $\frac{dy}{dx}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module