Gr12 Mathematics: Ch 5.3 Rules for Differentiation

What is the derivative of x^n with respect to x?

nx^n

x^(n+1)

nx^(n-1) (correct)

(n-1)x^n

What is the derivative of a constant k with respect to x?

kx

0 (correct)

-k

1

What is the derivative of k*f(x) with respect to x?

k*x*f(x)

k*f'(x) (correct)

f(x)*kx

f(x)/k

What is the derivative of f(x) + g(x) with respect to x?

f'(x) + g'(x) Signup and view all the answers

What is the derivative of f(x) - g(x) with respect to x?

f'(x) - g'(x) Signup and view all the answers

When should you use the first principles method for differentiation?

When the question specifically requests to use first principles or when asked to differentiate using the definition of a derivative Signup and view all the answers

What is the notation for the derivative of y = f(x) with respect to x?

All of the above Signup and view all the answers

What are the symbols D and d/dx called in differentiation?

Differential operators Signup and view all the answers

What is the general rule for differentiating x raised to the power of a real number?

d/dx[x^n] = nx^(n-1) Signup and view all the answers

What is the derivative of a constant multiple of a function?

k * d/dx[f(x)] Signup and view all the answers

Which of the following is a correct notation for the derivative of y with respect to x?

dy/dx Signup and view all the answers

When should you use the rules for differentiation?

When the question does not specify how to determine the derivative Signup and view all the answers

What is the derivative of the sum of two functions?

d/dx[f(x)] + d/dx[g(x)] Signup and view all the answers

What is the purpose of the differential operators D and d/dx?

To indicate the operation of differentiation Signup and view all the answers

What is the derivative of a function minus another function?

d/dx[f(x)] - d/dx[g(x)] Signup and view all the answers

Why do we use the rules for differentiation?

To simplify the process of finding derivatives Signup and view all the answers

What is the derivative of the function f(x) = 2x^3 with respect to x?

6x^2 Signup and view all the answers

If g(x) is a function, what is the derivative of f(x) = 3g(x) with respect to x?

3g'(x) Signup and view all the answers

What is the derivative of the function f(x) = x^2 + 2x with respect to x?

2x + 2 Signup and view all the answers

What is the notation for the derivative of the function y = f(x) with respect to x, where y is the dependent variable and x is the independent variable?

dy/dx Signup and view all the answers

What is the derivative of the function f(x) = x^4 - 2x^2 with respect to x?

4x^3 - 4x Signup and view all the answers

What is the purpose of the differential operators D and d/dx in differentiation?