Derivatives

Limit definition of the derivative practice problems f'(x) = \lim_{h\to 0}\frac{f(x+h) - f(x)}{h} 12 limit definition of the derivative practice problems with answers and step-by-step solutions, from linear functions to 1/x, √x and tangent lines. Power rule practice problems \frac{d}{dx}\,x^n = n\,x^{n-1} 12 power rule practice problems with answers and step-by-step solutions: polynomials, negative and fractional exponents, roots and tangent lines. Product and quotient rule practice problems (fg)' = f'g + fg', \qquad \left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^2} 12 product rule and quotient rule practice problems with answers and full step-by-step solutions, including triple products and a table problem. Derivatives of trig functions practice problems \frac{d}{dx}\sin x = \cos x, \quad \frac{d}{dx}\cos x = -\sin x, \quad \frac{d}{dx}\tan x = \sec^2 x 12 derivatives of trig functions practice problems with answers and full solutions: sin, cos, tan, sec, csc, cot, with product, quotient and chain rules. Chain rule practice problems \frac{d}{dx}\,f(g(x)) = f'(g(x))\,g'(x) 12 chain rule practice problems with answers and full step-by-step solutions, from (3x+1)⁵ to nested functions like sin²(4x) and e^(cos x). Derivatives of exponential and log functions practice problems \frac{d}{dx}e^x = e^x, \qquad \frac{d}{dx}\ln x = \frac{1}{x} 12 practice problems on derivatives of exponential and logarithmic functions, with answers and full solutions: e^x, a^x, ln x, log rules and x^x. Implicit differentiation practice problems \frac{d}{dx}\big[f(y)\big] = f'(y)\,\frac{dy}{dx} 12 implicit differentiation practice problems with answers and full solutions: circles, products, trig and exponentials, tangent lines and y''. Inverse trig derivatives practice problems \frac{d}{dx}\arcsin x = \frac{1}{\sqrt{1 - x^2}}, \qquad \frac{d}{dx}\arctan x = \frac{1}{1 + x^2} 12 inverse trig derivative practice problems with answers and full solutions: arcsin, arccos, arctan and arcsec with the chain and product rules.