Mathematics

Problem

### Passage V (Q. Nos. 58 to 60) Let

y = \int_{u(v)}^{v(x)} f(t) dt

, let us define

\frac{dy}{dx}

\frac{dy}{dx}

= v'(x) f^2(v(x)) - u'(x) f^2(u(x))

and the equation of the tangent at

(a, b)

and

y - b = \left(\frac{dy}{dx}\right)_{(a,b)} (x - a)

. If

f(x) = \int_{1}^{x} e^{t^{1/2}} (1 - t^2) dt

, then

\frac{d}{dx} f(x)

x = 1

is a. 0 b. 1 c. 2 d. -1