Medium
Find the derivative of $(5x^{3} + 3x - 1)(x - 1)$.
- A$20x^{3} - 15x^{2} + 6x - 4$
- B$20x^{3} - 15x^{2} + 6x - 2$
- C$15x^{3} - 15x^{2} + 6x - 4$
- D$20x^{3} + 15x^{2} + 6x - 4$
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Similar Questions
Find the derivative of the following function: $\frac{\cos x}{1+\sin x}$
Medium
View SolutionIf $f(x) = \begin{cases} x-5, & \text{for } x \leq 1 \\ 4x^2-9, & \text{for } 1 < x < 2 \\ 3x+4, & \text{for } x \geq 2 \end{cases}$,then $f^{\prime}(2^{+})$ is equal to:
$\frac{d}{dx} \log(\log x) =$
If $f(x) = 4x^3 + 3x^2 + 3x + 4$,$x \neq 0$,then $\frac{d}{dx}\left(x^3 \cdot f\left(\frac{1}{x}\right)\right) =$ . . . . . .
Match the functions in List-$I$ with their derivatives given in List-$II$.
List-$I$ List-$II$ $A$. $\sec^{-1} x$ $I$. $\frac{1}{1-x^2}, x \in (-1, 1)$ $B$. $\tanh^{-1} x$ $II$. $\frac{-1}{|x| \sqrt{x^2+1}}, x \neq 0$ $C$. $\coth^{-1} x$ $III$. $\frac{1}{|x| \sqrt{x^2-1}}, |x| > 1$ $D$. $\operatorname{cosech}^{-1} x$ $IV$. $\frac{1}{1-x^2}, x \in R - [-1, 1]$ $V$. $\frac{-1}{|x| \sqrt{1-x^2}}, |x| < 1, x \neq 0$
| List-$I$ | List-$II$ |
| $A$. $\sec^{-1} x$ | $I$. $\frac{1}{1-x^2}, x \in (-1, 1)$ |
| $B$. $\tanh^{-1} x$ | $II$. $\frac{-1}{|x| \sqrt{x^2+1}}, x \neq 0$ |
| $C$. $\coth^{-1} x$ | $III$. $\frac{1}{|x| \sqrt{x^2-1}}, |x| > 1$ |
| $D$. $\operatorname{cosech}^{-1} x$ | $IV$. $\frac{1}{1-x^2}, x \in R - [-1, 1]$ |
| $V$. $\frac{-1}{|x| \sqrt{1-x^2}}, |x| < 1, x \neq 0$ |
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