JEE Advanced · Mathematics

Differentiation

28 practice questions, each with the answer and an explanation.

Practise Differentiation now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 28 questions

If $f (x) = 2 x^{3} - 4 x^{2} + 5 x$ , what is $f^{'} (1)$ ?
If $f (x) = 3 x^{3} + 4 x$ , what is $f^{'} (3)$ ?
If $f (x) = 1 x^{3} + 3 x^{2} - 2 x$ , what is $f^{'} (3)$ ?
If $f (x) = 5 x^{3} - 3 x^{2} - 2 x$ , what is $f^{'} (- 2)$ ?
If $f (x) = 1 x^{3} - 5 x^{2} - 1 x$ , what is $f^{'} (4)$ ?
If $f (x) = 2 x^{3} + 4 x^{2} + 1 x$ , what is $f^{'} (2)$ ?
If $f (x) = 4 x^{3} + 4 x^{2} + 4 x$ , what is $f^{'} (1)$ ?
If $f (x) = 3 x^{3} - 5 x$ , what is $f^{'} (4)$ ?
If $f (x) = 1 x^{3} - 4 x^{2} + 5 x$ , what is $f^{'} (0)$ ?
If $f (x) = 4 x^{3} + 4 x^{2} - 4 x$ , what is $f^{'} (4)$ ?
If $f (x) = 4 x^{3} - 5 x^{2} - 3 x$ , what is $f^{'} (4)$ ?
If $f (x) = 4 x^{3} - 2 x^{2} - 1 x$ , what is $f^{'} (0)$ ?
If $f (x) = 1 x^{3} - 1 x^{2} - 5 x$ , what is $f^{'} (4)$ ?
If $f (x) = 2 x^{3} + 3 x^{2} - 2 x$ , what is $f^{'} (2)$ ?
If $f (x) = 4 x^{3} + 4 x^{2} + 5 x$ , what is $f^{'} (4)$ ?
If $f (x) = 3 x^{3} + 2 x^{2} + 4 x$ , what is $f^{'} (3)$ ?
If $f (x) = 1 x^{3} + 4 x^{2} - 5 x$ , what is $f^{'} (3)$ ?
If $f (x) = 2 x^{3} - 3 x^{2} + 1 x$ , what is $f^{'} (3)$ ?
If $f (x) = 3 x^{3} - 4 x$ , what is $f^{'} (- 2)$ ?
If $f (x) = 4 x^{3} - 4 x^{2}$ , what is $f^{'} (- 1)$ ?
If $f (x) = 2 x^{3} + 3 x^{2} + 4 x$ , what is $f^{'} (- 1)$ ?
If $f (x) = 3 x^{3} + 6 x^{2} + 1 x$ , what is $f^{'} (3)$ ?
If $f (x) = 4 x^{3} - 1 x^{2} - 1 x$ , what is $f^{'} (0)$ ?
If $f (x) = 5 x^{3} - 3 x^{2} - 1 x$ , what is $f^{'} (4)$ ?
Let $f (x) = x^{3} - 3 x + 1$ . How many real solutions does the equation $f (f (x)) = 0$ have?
What is the smallest real constant $c$ such that $ln x \leq c x$ for every $x > 0$ ?
What is $x \to 0 lim \frac{e ^{x^{2}} - cos x - \frac{3}{2} x ^{2}}{x ^{4}}$ ?
A differentiable function $f$ satisfies $f (x + y) = f (x) + f (y) + x y (x + y)$ for all real $x, y$ , and $f^{'} (0) = - 1$ . What is $f (6)$ ?

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