AP EAMCET Differentiation Rules — practice questions
70 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAMCET Differentiation Rules in the app →A sensor reads a fixed value of 7 units at all times. Its rate of change with respect to time isApplying the power rule to y = x^5 gives dy/dx equal toThe expression 12x^3 is the slope function of which curve?Which function gives cos x when differentiated once?Cosine falls where sine is positive, so d(cos x)/dx equalsWriting tan x as sin x over cos x, the quotient rule yieldsOnly one of these functions equals its own derivative. Which one?The natural logarithm has slope 1/x at each positive x, so its slope function isFor a constant a > 0, differentiating the exponential a^x with respect to x givesWriting cot x as cos x over sin x, the derivative comes out asTreating sec x as 1/cos x, the reciprocal rule gives its slope function asSetting y = sin^-1 x gives x = sin y, which leads to dy/dx equal toFrom x = tan y, the slope of the inverse tangent curve at x isSince cos^-1 x = pi/2 - sin^-1 x, its derivative on (-1, 1) isA square root function y = sqrt(x) with x > 0 has slope functionThe reciprocal function 1/x, for nonzero x, changes at the rateWhich expression is the product rule for the derivative of two functions u and v multiplied together?For the ratio u/v with v nonzero, the quotient rule numerator isIf y depends on u and u depends on x, the chain rule states that dy/dx equalsA curve is y = x sin x. Its slope function isA growth model follows y = x^2 e^x. Its rate of change with x isA wave is modelled by y = sin(2x). Its slope at x isA cell count follows y = e^(3x). The count changes at the rateThe slope of y = ln(5x) for positive x does not depend on the 5 because it equalsA cubic power of a quadratic, y = (x^2 + 1)^3, has slope functionA distance is given by y = sqrt(1 + x^2). Its rate of change with x isSimplified, the slope of y = x/(x + 1) away from x = -1 isThe sinc-like curve y = (sin x)/x, for x nonzero, has slope functionA variable base and exponent give y = x^x for x > 0. Its derivative isFor the cubic x^3 - 3x, the number of real points with a flat tangent isA cube has volume V = x^3 for edge x. At x = 2, how fast does V change per unit edge?A tangent touches the parabola y = x^2 at x = 3. How steep is it?The parabola y = x^2 - 4x + 5 has a level tangent line at x equal toAt the origin, the sine curve climbs with slopeThe V-shaped function f(x) = |x| at x = 0 isDifferentiating x^4 twice in a row givesThe curvature-type quantity d^2y/dx^2 for y = sin x equalsEach differentiation of e^(2x) multiplies it by 2, so the second derivative isAfter three differentiations of y = x^3, what remains?Differentiating sin x four times returns which function?Besides f(a) = f(b) and continuity on [a, b], Rolle's theorem needsWho gave the first general proof of Rolle's theorem, in 1823?Which Indian mathematician of the 12th century stated an early form of Rolle's theorem?The parabola f(x) = x^2 - 4x takes equal values at 0 and 4. Rolle's point c isBoth ends of [2, 4] give 0 for f(x) = x^2 - 6x + 8. Rolle's theorem locates c atRolle's theorem cannot be applied to |x| on [-1, 1] becauseRolle's theorem is a special case of which theorem?Rolle's theorem depends on which property of the real numbers?In which year did Leibniz introduce his differential quotient notation dy/dx?In Newton's dot notation, a dot over a symbol stands forLeibniz notation presents the derivative in the form ofPrime notation marks the derivative of f byTo get the partial derivative of f(x, y) in x, the variable y is keptHolding y fixed, the partial derivative of f(x, y) = x^2 y in x isRepeated differentiation of a function yields derivatives calledAt a point, the derivative of a function measures theA constant function has derivative zero since its tangent line isWhich statement about continuity and differentiability is correct?Taking logarithms of a product before differentiating turns it intoFor y = x^(sin x), the most convenient method isIf y = u/v, then ln y on the right side equalsThe curve y = ln(sin x), where sin x is positive, has slope functionA bell-type curve y = e^(x^2) changes with x at the rateThe common logarithm y = log10 x, for x > 0, has slope functionSquaring the sine, y = sin^2 x, gives a slope function equal toThe curve y = x e^x has slope at the origin equal toFor positive x, the product x^3 ln x has slope functionRewriting 1/x^2 as x^(-2), its derivative becomesFor f(x) = 2x^3 - 5x + 1, the slope at x = 1 isNear a point, the derivative supplies which kind of approximation of the function?