Key rules include the power rule, product rule, quotient rule, and chain rule. Mastering these is fundamental for simplifying complex derivatives.
The chain rule helps differentiate composite functions. If y = f(g(x)), then dy/dx = f(g(x)) * g(x). Break down the composite function into simpler parts.
The product rule is used when differentiating the product of two functions. If y = u(x)v(x), then dy/dx = u(x)v(x) + u(x)v(x).
Remember the derivatives of basic trig functions (sin x, cos x, tan x, etc.). Use trigonometric identities to simplify expressions before and after differentiation.
The quotient rule applies when differentiating a function that is the ratio of two other functions. If y = u(x)/v(x), then dy/dx = [v(x)u(x) - u(x)v(x)] / [v(x)]^2.
Know the derivatives of e^x and ln(x). Use properties of logarithms to simplify expressions before differentiating, especially when dealing with complex exponents.
Differentiate both sides of the equation with respect to x, treating y as a function of x. Use the chain rule when differentiating terms involving y. Solve for dy/dx.
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