The Purplemath Forums

I am having trouble finding the derivative of cubed root of x using only limits. I know it is easy to use chain rule but I cannot use that yet.

I'm sorry, I meant the cube root of x. as in cuberoot(x).

So far a tried finding the derivative with a limit as h approaches 0
lim h-->0[(cuberoot(a+h) - cuberoot(a)) / ((a+h) - a)]

With this, I always end up with an indeterminate form.

I'm sorry, I meant the cube root of x. as in cuberoot(x). So far a tried finding the derivative with a limit as h approaches 0 lim h-->0[(cuberoot(a+h) - cuberoot(a)) / ((a+h) - a)] With this, I always end up with an indeterminate form. \lim_{h\to0}\frac{\sqrt[3]{a+h}-\sqrt[3]{a}}{h} use the fact t...

Find constants A and B such that the function y = Asin(x) + Bcos(x) satisfies the differential equation y" + y' - 2y = sin(x)

I can find the derivatives just fine, but I'm not sure where to go in order to solve for A or B.

y'(x) = Acosx - Bsinx
y"(x) = -Asinx - Bcosx

(-Asinx - Bcosx) + (Acosx - Bsinx) - 2(Asinx + Bcosx) = sinx

From here I'm not sure how to solve for A or B since there are 2 unknowns and only 1 equation

Find y" by implicit differentiation x^3 + y^3 = 1 Here's my work: 3x^2 + 3y^2y' = 0 y' = (-3x^2)/(3y^2) = (-x^2)/(y^2) y" = (-2xy^2 + 2x^2y(dy/dx)) / y^4 = 2(-xy - x^4y^-2) / y^3 The back of the book says that the answer is -2x / y^5. I don't understand how they're simplifying it to that. ...

Ah I see. Thank you.

I am having difficulty finding integral((tanx)^2 / (secx)^2)dx.

I tried converting everything in terms of sinx and cosx but that doesn't seem to help.

I am having difficulty finding integral((tanx)^2 / (secx)^2)dx. I tried converting everything in terms of sinx and cosx but that doesn't seem to help. Once you've simplified and gotten an expression in just sine, you can use the double-angle formula (in reverse) for the cosine: . . . . . \sin^2(...

I know how to complete the square to solve for roots of a non-factorable quadratic, but I don't understand the way my math book uses it to simplifiy non-factorable quadratics.. for example, the book states that "To integrate the function we complete the square in the denominator 4x^2 - 4x + 3 =...