Differentiation techniques: A checklist for H2 Math success

Differentiation techniques: A checklist for H2 Math success

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Frequently Asked Questions

The Power Rule states that if f(x) = x^n, then f(x) = nx^(n-1). Its applied by multiplying the original exponent by the variable and then reducing the exponent by one.
The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x).
The Chain Rule is used to differentiate composite functions. If y = f(g(x)), then dy/dx = f(g(x)) * g(x). Use it when you have a function inside another function.
The Product Rule is used to differentiate the product of two functions. If y = u(x)v(x), then dy/dx = u(x)v(x) + u(x)v(x).
The Quotient Rule is used to differentiate the quotient of two functions. If y = u(x)/v(x), then dy/dx = [v(x)u(x) - u(x)v(x)] / [v(x)]^2. Its necessary when you have one function divided by another.
If y = a^x, then dy/dx = a^x * ln(a). Remember to use the chain rule if the exponent is a function of x.
Implicit differentiation is used when y is not explicitly defined as a function of x. Differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx.
If y = ln(x), then dy/dx = 1/x. If y = log_a(x), then dy/dx = 1/(x*ln(a)). Remember to apply the chain rule if the argument of the logarithm is a function of x.
Common mistakes include forgetting the chain rule, misapplying the product or quotient rule, incorrect differentiation of trigonometric functions (signs), and errors in algebraic simplification after differentiation.