If a problem is solved. It is not 'the' answer.
No attempt is made to search for the most elegant answer.
I highly recommend that you at least try to solve the
problem before you read the solution.
y = 5x ; y' = 5 y = x^{3} ; y' = 3x^{2} y = (2x^{2}+ x + 5) ; y'= 4x + 1 x - 1 (x+1).1 - (x-1).1 2 y = ------- ; y' = -------------------- = ------------------ x + 1 (x+1)(x+1) (x+1)(x+1) y = (x+5)^{6} ; y' = 6.(x+5)^{5} y = (2x + 6)^{3} ; y' = 3.(2x + 6)^{2}.2 y = (2x + 6)(5x - 7) ; y'= 2.(5x - 7) + (2x + 6).5 y = (2x + 6)^{2}.(5x - 7)^{3}; y'= 2.(2x + 6).2.(5x - 7)^{3}+ (2x + 6)^{2}.3.(5x - 7)^{2}.5 y = x/5 ; y' = 1/5 1 y = 5/x ; y' = -5.--- x.x 7 y = --- <=> y = 7.x^{-4} ; y' = -28 x^{-5} x^{4}
Calculate the derivative of ax + b y = --------- cx + d |
Calculate the derivative of ad - bc y = ---------------- (cx + d)(cx + d) |
Calculate the first and second derivative of x.x + x + 1 y = ------------- x + 1 |
Calculate the first and second derivative of y = sqrt(x^{3}-3x +2) |
Calculate the first and second derivative of y = sin(2x) - cos(2x) |
An area A depends on x in the following way. 2r^{3}.x^{3} A = -------------- with r = constant. (x^{2} + r^{2})^{2} Calculate A'. |
Find 1 - sqrt(cos(x)) lim ------------------ 0 x^{2} |
Find x(2x + 3)x - 1 lim ------------------- -1 x^{3} - 3x - 2 |
sin(3x) + tan(2x) Find lim ------------------ 0 x - 2 sin(x) |
x^{3} e^{x} + 2x^{2} - 3 Find lim -------------------- + infty x^{2} - e^{2x} + 5 |
The numbers a and x are positive. Find : x sqrt(x) - a sqrt(a) lim ------------------------- a sqrt(x) - sqrt(a) |
x^{2} + 2px + q Given : y = -------------- x^{2} + 1 Prove that there are two x values, x' and x", such that y' = 0. Then prove that x'.x" = -1. |
The derivative of f(x) is f'(x). The derivative of f'(x) is f"(x) an is called the second derivative of f(x). The derivative of f"(x) is f"'(x) an is called the third derivative of f(x). ... Now, let f(x) = sqrt(x) n-1 (2n-2)! (1-2n)/2 Prove that the n-th derivative of f(x) = (-1) .--------.(4x) (n-1)! |
Find lim (x. sin(3/x)) x -> infty |
The function f(x) = ( (x-2)^{2} )^{1/3} - 3 is given in interval [1,3]. Investigate whether or not we can apply Rolle's theorem. |
The function e^{x}.sin(x) satisfies the three conditions of Rolle's theorem in [0,pi]. Find point P(c,f(c)) such that f'(c) = 0. |