JEE Main Mathematics: Calculus (Differentiation) Practice Questions

12 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$Find the derivative of f(x) = 10.$
Easy
Q2.
$Find the derivative of f(x) = sin(x) + cos(x).$
Easy
Q3.
$If f(x) = ln(x), what is f'(x)?$
Easy
Q4.
$W ha t i s t h e d er i v a t i v eo f f (x) = e^{x} + 3 x ?$
Easy
Q5.
$W ha t i s t h e d er i v a t i v eo f f (x) = x^{5} w i t h r es p ec tt o x ?$
Easy
Q6.
$T h e d er i v a t i v eo f t a n^{-} 1 (s q r t ((1 - cos x) / (1 + cos x))) w i t h r es p ec tt o x i s$
Medium
Q7.
$If y = x^x^x... up to infinity, then dy/dx is equal to$
Medium
Q8.
$If x = a(theta + sin theta) and y = a(1 - cos theta), then dy/dx at theta = pi/2 is$
Medium
Q9.
$If y = log(sec x + tan x), then dy/dx is$
Medium
Q10.
$Let f(x) = |x-1| + |x-2| + |x-3|. The number of points where f(x) is not differentiable is:$
Hard
Q11.
$Let f(x) be a differentiable function such that f(x + y) = f(x) + f(y) + xy(x + y) for all x, y in R. If f'(0) = 1, then find the value of f(1).$
Hard
Q12.
$I f x = a (cos t + t s in t) an d y = a (s in t - t cos t), t h e n d^{2} y / d x^{2} a tt = p i /4 i s :$
Hard

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