If `f(x) = sin^2x`, evaluate `f'(pi/3)` starting from definition of differential coefficient.

If f(x) = e^x , find f' (3) starting from defination

If f(x) = |sin x - cosx| , find f' ( pi//6)

If f(x) =x^2+2x+7 , find f'(3).

If f(x) = |sinx| + | cos x| , find f'((3pi)/(4))

If f(x) = sin x and g(x) = 2x, find fog.

If f(x) = 3(2x + 3)^(2//3) + 2x + 3 , then: (a) f(x) is continuous but not differentiable at x = - (3)/(2) (b) f(x) is differentiable at x = 0 (c) f(x) is continuous at x = 0 (d) f(x) is differentiable but not continuous at x = - (3)/(2)

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x)=2ax +sin2x, then the set of values of a for which f(x) is one-one and onto is

Consider a real-valued function f(x)= sqrt(sin^-1 x + 2) + sqrt(1 – sin^-1x) then The domain of definition of f(x) is

Given, f(x)= sin^(3) x and P(x) is a quadratic polynomial with coefficient unity. Statement I int_(0)^(2pi) P(x).f''(x) dx vanishes. Statement II int _(0)^(2pi) f (x) dx vanishes.

f(x) = sin x is a strictly decreasing in (pi/2,pi)