Method of DifferentiationeasyFree

Method of Differentiation: Equal

JEE Maths question with a full step-by-step solution.

Question
If f′(x)=3x2+6f'(x) = \sqrt{3x^2+6} and y=f(x3)y = f(x^3), then at x=1x = 1, (dydx)\left(\dfrac{dy}{dx}\right) is equal to.
Solution
Answer: 9
Step 1: Apply the chain rule
dydx=f′(x3)⋅3x2\frac{dy}{dx} = f'(x^3)\cdot 3x^2
 Step 2: Evaluate at x=1x = 1
dydx∣x=1=f′(1)⋅3=3(1)2+6⋅3=9⋅3=9\left.\frac{dy}{dx}\right|_{x=1} = f'(1)\cdot 3 = \sqrt{3(1)^2+6}\cdot 3 = \sqrt{9}\cdot 3 = 9
 Answer: 9
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