AP EAPCET (Engineering) Differentiation — practice questions
80 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Differentiation in the app →$\dfrac{d}{dx}(x^n)$ equals:$\dfrac{d}{dx}( in x)$ equals:$\dfrac{d}{dx}(e^x)$ equals:$\dfrac{d}{dx}(\ln x)$ equals:The **chain rule** states $\dfrac{dy}{dx}$ for $y = f(g(x))$ is:The product rule for $\dfrac{d}{dx}(uv)$ is:$\dfrac{d}{dx}(\tan x)$ equals:$\dfrac{d}{dx}( in^{-1} x)$ equals:If $y = in(\cos x)$, then $\dfrac{dy}{dx}$ equals:If $y = x^x$, then $\dfrac{dy}{dx}$ equals:If $y = \log( in x)$, then $\dfrac{dy}{dx}$ equals:$\dfrac{d}{dx}(a^x)$ equals (where $a > 0$):If $x^2 + y^2 = 25$, then $\dfrac{dy}{dx}$ equals:If $x = a t^2$, $y = 2 a t$ (parametric), then $\dfrac{dy}{dx}$ equals:If $y = in x$, then $y_n = \dfrac{d^n y}{dx^n}$ at $x = 0$ for $n = 4$ equals:If $y = \tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$, then $\dfrac{dy}{dx}$ equals:If $y = x in x$, then $y_2 = \dfrac{d^2y}{dx^2}$ equals:If $x^y = y^x$, then $\dfrac{dy}{dx}$ equals:If $y = in^{-1}(2x qrt{1-x^2})$ for $-1/ qrt 2 < x < 1/ qrt 2$, then $\dfrac{dy}{dx}$ equals:$\dfrac{d}{dx}\left[\log(\log x)\right]$ at $x = e^e$ equals:If $y = ( in x)^x$, then $\dfrac{dy}{dx}$ equals:Given $x = a(\theta - in\theta)$, $y = a(1 - \cos\theta)$ (cycloid). Then $\dfrac{dy}{dx}$ equals:If $y = e^x \cos x$, then $\dfrac{d^2 y}{dx^2} - 2\dfrac{dy}{dx} + 2y$ equals:If $f(x) = |x - 1| + |x - 3|$, then $f'(2)$ equals:If $y_n$ denotes the $n$-th derivative of $y = in x$, then $y_n = $:If $f(x) = x^3 - 3x$, the values of $x$ where $f'(x) = 0$ are:$\dfrac{d}{dx}\left[\cos^{-1}\left(\dfrac{1-x^2}{1+x^2}\right)\right]$ for $x > 0$ equals:Find d/dx of tan x where it is defined.Differentiate the natural logarithm ln x for x greater than 0.For a constant a > 0, what is d/dx of a^x?What is d/dx of x^2 e^x?What is the derivative of ln(3x - 2) where 3x - 2 > 0?For a composite function f(g(x)), the chain rule gives its derivative as which product?In integration, which technique is the counterpart of the chain rule?The chain rule is the basis of which algorithm used to train neural networks?Which formula extends the chain rule to higher-order derivatives?If g(x) = e^x has inverse f(y) = ln y, what is f'(y) by the inverse rule?Applying the chain rule to the reciprocal of g(x), what is d/dx of 1/g(x)?Why take logarithms before differentiating some expressions?Using logarithmic differentiation, find d/dx of x^x for x greater than 0.Find d/dx of x^(sin x) for x > 0 using logarithms.In logarithmic differentiation, what does ln do to a power u^v?The derivative of f at a is the limit of what expression as h tends to 0?The speed of a car at an instant is the derivative of which quantity with respect to time?What is the process of finding a derivative called?Which statement on differentiability and continuity is true?The function f(x) = |x| at x = 0 is best described as which of these?Differentiability at a needs which two one-sided values to match?Which rule gives the nth derivative of a product of two functions?The general Leibniz integral rule is derived using which result?The logarithmic derivative of a function f(x) equals which expression?If f(x) = x^2 sin x, what is f'(0)?What is the value of d/dx (tan x) at x = pi/4?What is the derivative of log to base a of x, for x > 0 and a > 0, a not 1?Using linearity, find d/dx of 3 sin x + 2 cos x.The derivative of x^5 with respect to x isDifferentiating the constant function y = 9 with respect to x givesWhat is the slope function of y = 1/x for x not 0?If y = sqrt(x) with x > 0, what is dy/dx?The derivative of sin^-1 x on the interval (-1, 1) isFind the derivative of x^x for x > 0.Which expression is the derivative of cosec x?If y = x^4, then the value of d2y/dx2 at x = 1 isThe tangent to the curve y = x^2 - 4x is horizontal at x equal toThe function f(x) = x^3 - 3x has a local minimum at x equal toDifferentiate sqrt(x^2 + 1) with respect to x.For x = t^2 and y = t^3 with t not 0, dy/dx equalsFor x = 2t and y = t^2, the value of dy/dx isThe function f(x) = |x| fails to be differentiable at x equal toA function that has a derivative at a point must also beWhich function is continuous at x = 0 but not differentiable there?A function with infinitely many derivatives is calledDifferentiating a polynomial again and again eventually givesWhich derivative notation is named after Gottfried Leibniz?The discrete counterpart of differentiation isThe function y = x^(1/3), inverse of x^3, is not differentiable atLogarithmic differentiation is useful mainly because logarithmsIf f is differentiable, then d/dx of 5f(x) equalsFor x not equal to 0, d/dx of x^-2 equalsThe derivative of ln x at x = 2 is