Question
If $f^{\prime}(x)=x^{-1}$, then find $f(x)$
✓
Answer
$\begin{aligned} f^{\prime}(x) & =\frac{1}{x} \\ \therefore f(x) & =\int \frac{1}{x} d x \\ & =\log x+c \text { (c is a constant) }\end{aligned}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Evaluate the following:
→$\int \frac{\sin (\log x)^2}{x} \cdot \log x d x$
Determine the values of $c$ that satisfy $|c \bar{u}|=3, \bar{u}=\hat{i}+2 \hat{j}+3 \hat{k}$
→Solve the following differential equations.
→$y-x \frac{d y}{d x}=0$
Write the degree of the following differrntial equation?
$5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}-\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-6\text{y}=\log\text{x}$
→$5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}-\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-6\text{y}=\log\text{x}$
Write the negations of the following.Ǝ x ∈ N such that x – 17 < 20
State which of the following are not the probability mass function of a random variable. Give reasons for your answer : 
Write the duals of each of the following. (p ∨ q) ∧ (r ∨ s)
Diffrentiate the following w. r. t. x.
$\cos ^3\left[\cos ^{-1}\left(x^3\right)\right]$
→$\cos ^3\left[\cos ^{-1}\left(x^3\right)\right]$
Evaluate: $\int_0^1 \frac{ e ^x}{\sqrt{ e ^x-1}} d x$
→Using rules of negation write the negations of the following with justification. (~ p ∨ ~q) ∨ (p ∧ ~q)