alleryStart learning →$\dfrac{d}{dx}(x^n)$ equals:
- $x^{n-1}$
- $n x^n$
- $n x^{n-1}$
- $(n-1) x^n$
Show answer and solution
Correct answer: C. $n x^{n-1}$
Power rule: $\frac{d}{dx}(x^n) = n x^{n-1}$ for any real $n$.
KEAM Differentiation — practice questions
Explore 29 free Differentiation questions in KEAM Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Differentiation with Quill →Differentiation questions and exercises with answers
Showing questions 1–29 of 29.
$\dfrac{d}{dx}(x^n)$ equals:Read the answer and worked solution →$\dfrac{d}{dx}(\sin x)$ equals:Read the answer and worked solution →$\dfrac{d}{dx}(e^x)$ equals:Read the answer and worked solution →$\dfrac{d}{dx}(\ln x)$ equals:Read the answer and worked solution →The **chain rule** states $\dfrac{dy}{dx}$ for $y = f(g(x))$ is:Read the answer and worked solution →The product rule for $\dfrac{d}{dx}(uv)$ is:Read the answer and worked solution →$\dfrac{d}{dx}(\tan x)$ equals:Read the answer and worked solution →$\dfrac{d}{dx}(\sin^{-1} x)$ equals:Read the answer and worked solution →If $y = \sin(\cos x)$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →If $y = x^x$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →If $y = \log(\sin x)$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →$\dfrac{d}{dx}(a^x)$ equals (where $a > 0$):Read the answer and worked solution →If $x^2 + y^2 = 25$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →If $x = a t^2$, $y = 2 a t$ (parametric), then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →If $y = \sin x$, then $y_n = \dfrac{d^n y}{dx^n}$ at $x = 0$ for $n = 4$ equals:Read the answer and worked solution →If $y = \tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →If $y = x \sin x$, then $y_2 = \dfrac{d^2y}{dx^2}$ equals:Read the answer and worked solution →If $x^y = y^x$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →If $y = \sin^{-1}(2x\sqrt{1-x^2})$ for $-1/\sqrt 2 < x < 1/\sqrt 2$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →$\dfrac{d}{dx}\left[\log(\log x)\right]$ at $x = e^e$ equals:Read the answer and worked solution →If $y = (\sin x)^x$, then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →Given $x = a(\theta - \sin\theta)$, $y = a(1 - \cos\theta)$ (cycloid). Then $\dfrac{dy}{dx}$ equals:Read the answer and worked solution →If $y = e^x \cos x$, then $\dfrac{d^2 y}{dx^2} - 2\dfrac{dy}{dx} + 2y$ equals:Read the answer and worked solution →If $f(x) = |x - 1| + |x - 3|$, then $f'(2)$ equals:Read the answer and worked solution →If $y_n$ denotes the $n$-th derivative of $y = \sin x$, then $y_n = $:Read the answer and worked solution →If $f(x) = x^3 - 3x$, the values of $x$ where $f'(x) = 0$ are:Read the answer and worked solution →$\dfrac{d}{dx}\left[\cos^{-1}\left(\dfrac{1-x^2}{1+x^2}\right)\right]$ for $x > 0$ equals:Read the answer and worked solution →True or False: Derivatives (ISC 12)Read the answer and worked solution →Match the Derivative (ISC 12)Read the answer and worked solution →
Worked practice questions
$\dfrac{d}{dx}(\sin x)$ equals:
- $-\sin x$
- $-\cos x$
- $\cos x$
- $\sec^2 x$
Show answer and solution
Correct answer: C. $\cos x$
Standard result: $d/dx(\sin x) = \cos x$.
$\dfrac{d}{dx}(e^x)$ equals:
- $e^x$
- $\ln x$
- $x e^{x-1}$
- $1/x$
Show answer and solution
Correct answer: A. $e^x$
$e^x$ is its own derivative — unique property of the exponential function.
How to practise
- Choose a Differentiation question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.