JEE Main · Mathematics

Differentiation

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

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

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If $f (x) = 5 x^{3} - 4 x^{2} + 5 x$ , what is $f^{'} (3)$ ?
If $f (x) = 1 x^{3} + 5 x^{2} - 5 x$ , what is $f^{'} (1)$ ?
If $f (x) = 1 x^{3} + 3 x^{2} - 3 x$ , what is $f^{'} (3)$ ?
If $f (x) = 4 x^{3} + 2 x^{2} - 3 x$ , what is $f^{'} (2)$ ?
If $f (x) = 4 x^{3} + 5 x$ , what is $f^{'} (0)$ ?
If $f (x) = 5 x^{3} + 3 x^{2} + 3 x$ , what is $f^{'} (1)$ ?
If $f (x) = 1 x^{3} - 4 x$ , what is $f^{'} (1)$ ?
If $f (x) = 2 x^{3} - 2 x^{2} - 2 x$ , what is $f^{'} (2)$ ?
If $f (x) = 1 x^{3} - 1 x^{2} + 3 x$ , what is $f^{'} (2)$ ?
If $f (x) = 3 x^{3} + 5 x^{2} - 1 x$ , what is $f^{'} (2)$ ?
If $f (x) = 2 x^{3} - 6 x^{2} + 1 x$ , what is $f^{'} (- 1)$ ?
If $f (x) = 2 x^{3} - 2 x^{2} + 4 x$ , what is $f^{'} (1)$ ?
If $f (x) = 5 x^{3} - 2 x^{2} + 4 x$ , what is $f^{'} (2)$ ?
If $f (x) = 3 x^{3} - 4 x^{2}$ , what is $f^{'} (0)$ ?
If $f (x) = 5 x^{3} - 2 x^{2} - 5 x$ , what is $f^{'} (2)$ ?
If $f (x) = 1 x^{3} + 6 x^{2} + 1 x$ , what is $f^{'} (- 2)$ ?
If $f (x) = 1 x^{3} - 3 x^{2} - 4 x$ , what is $f^{'} (4)$ ?
If $f (x) = 2 x^{3} - 4 x^{2}$ , what is $f^{'} (- 2)$ ?
If $f (x) = 1 x^{3} + 3 x^{2} - 3 x$ , what is $f^{'} (0)$ ?
If $f (x) = 2 x^{3} + 3 x^{2} - 2 x$ , what is $f^{'} (0)$ ?
If $f (x) = 5 x^{3} - 6 x^{2}$ , what is $f^{'} (- 1)$ ?
If $f (x) = 3 x^{3} + 5 x^{2} + 5 x$ , what is $f^{'} (3)$ ?
If $f (x) = 1 x^{3} - 3 x^{2} - 3 x$ , what is $f^{'} (0)$ ?
If $f (x) = 2 x^{3} - 3 x^{2} - 2 x$ , what is $f^{'} (2)$ ?
If $f (x) = 2 x^{3} + 5 x^{2} + 2 x$ , what is $f^{'} (1)$ ?
If $f (x) = 3 x^{3} - 2 x$ , what is $f^{'} (2)$ ?
If $f (x) = 2 x^{3} - 6 x^{2} + 4 x$ , what is $f^{'} (0)$ ?
If $f (x) = 3 x^{3} - 6 x^{2} + 1 x$ , what is $f^{'} (4)$ ?
If $f (x) = 3 x^{3} + 2 x$ , what is $f^{'} (- 1)$ ?
If $f (x) = 1 x^{3} + 1 x$ , what is $f^{'} (3)$ ?
The curve $x^{2} + x y + y^{2} = 7$ passes through the point $(2, 1)$ . What is $\frac{d ^{2} y}{d x ^{2}}$ at that point?
For how many integer values of $b$ can exactly three distinct tangents be drawn to the curve $y = x^{3} - 3 x$ from the point $(2, b)$ ?

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