Use logarithmic differentiation to find the derivative of the function. $y=x^{6 x}$
A) $y^{\prime}=6(\ln x+1)$
B) $y^{\prime}=6 x^{6 x}(\ln x+1)$
C) $y^{\prime}=-6 x^{6 x}(\ln x+6)$
D) $y^{\prime}=6 x^{6 x}(6 \ln x+1)$
E) $y^{\prime}=x^{x}(\ln 6 x+1)$

Question

Quizplus · Accepted Answer

Using logarithmic differentiation, we have:$$\ln y = \ln x^{6x} = 6x \ln x$$Differentiating both sides with respect to $x$, we get:$$\frac{y'}{y} = 6(\ln x + 1)$$Multiplying both sides by $y = x^{6x}$, we get:$$y' = 6x^{6x}(\ln x + 1)$$

Use Logarithmic Differentiation to Find the Derivative of the Function y=x6xy=x^{6 x}y=x6x

Use Logarithmic Differentiation to Find the Derivative of the Function $y=x^{6 x}$