frac{d}{dx}(5^{log x}) = dots | vedclass

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

Question

(A) Let $y = 5^{\log x}$.Using the property $a^{\log_b c} = c^{\log_b a}$, we can write $y = x^{\log 5}$.Now, differentiate with respect to $x$ using

Vedclass · Accepted Answer

$\frac{5^{\log x} \ln 5}{x}$

Vedclass · Answer

(A) Let $y = 5^{\log x}$.Using the property $a^{\log_b c} = c^{\log_b a}$, we can write $y = x^{\log 5}$.Now, differentiate with respect to $x$ using the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$:$\frac{dy}{dx} = (\log 5) x^{\log 5 - 1}$.Alternatively, using the chain rule for $y = 5^{\log x}$:$\frac{dy}{dx} = 5^{\log x} \cdot \ln 5 \cdot \frac{d}{dx}(\log x) = 5^{\log x} \cdot \ln 5 \cdot \frac{1}{x} = \frac{5^{\log x} \ln 5}{x}$.Since $\ln 5$ is equivalent to $\log_e 5$, the correct expression is $\frac{5^{\log x} \ln 5}{x}$.

$\frac{d}{dx}(5^{\log x}) = \dots$

Similar Questions

If $f(x) = \log_{(x^2-2x+1)}(x^2-3x+2)$, $x \in R - \{1, 2\}$ and $x \neq 0$, then $f'(3) =$

The value of $\log _{e} 2 \cdot \frac{d}{dx}(\log _{\cos x} \operatorname{cosec} x)$ at $x=\frac{\pi}{4}$ is.

The derivative of $\log_8(\log_5 x)$ with respect to $x$ is:

Let $f(x)=e^x$, $g(x)=\sin^{-1} x$ and $h(x)=f(g(x))$, then $\frac{h'(x)}{h(x)}$ is equal to

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module