Limits and Deri...

is equal to

is equal  to

The derivative of f(x) = 1 + x + x² + x³ + ..... + x¹⁰⁰ at x = 1 is

is equal to

If x = a cos⁴and y = a sin⁴, then  at  =  is equal to

If f(X) = xⁿ +a x^n-1 + a² x^n-2 +… +a^n-1 x + aⁿ for some fixed real number, then f'(x) is equal to 

If y = x⁵ cotx, then dy/dx is equal to

 is equal to

 _{is equal to}

If y = a e^mx + b e ^-mx, then y_^'' is equal to

The derivative of f(x) = |x| at x = 0 is

, n  N, is equal to

If f(x) = (x – 2)² (2x – 3), then find the value of f'(1).

What will be the derivative of  (x sin x + cos x)(x cos x – sin x)?

If y = , find the value of .

If x = , y = , then  equals

If y = (x + 1)(x + 2)(x + 3), then dy/dx is equal to

 is equal to

If f(x) = x sin x, then f' is equal to

Find (6x³ + 19x² + 14x + 18)/(5x³ + 6x² + 7x + 12).