AP

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let y=e1+2x2y=e^{\sqrt{1+2x^{2}}}. (i) Derive an exact expression for dydx\dfrac{dy}{dx} in its simplest form. (ii) Evaluate dydx\dfrac{dy}{dx} at x=0x=0. (iii) Using your result from part (i), find the limit lim⁡x→0e1+2x2−ex,\lim_{x\to0}\frac{e^{\sqrt{1+2x^{2}}}-e}{x}, and write the answer in terms of ee.

Related theory

Browse the problem library