Derivatives using Power and Product rule

Front

What is the Power Rule for differentiation?

Back

The Power Rule states that if y = x^n, then the derivative dy/dx = n*x^(n-1).

Front

What is the Product Rule for differentiation?

Back

The Product Rule states that if y = u*v, then the derivative dy/dx = u'v + uv', where u and v are functions of x.

Front

Find the derivative of y = 2x^2(3x - 4) using the Product Rule.

Back

2x^2(3) + (3x - 4)(4x) = 6x^2 + 12x^2 - 16x = 18x^2 - 16x.

Front

What is the derivative of y = (x - 1)(x + 2)?

Back

dy/dx = (1)(x + 2) + (x - 1)(1) = 2x + 1.

Front

Find the derivative of y = (3x^2 + 2x)(5x - 1).

Back

dy/dx = (6x + 2)(5x - 1) + (3x^2 + 2x)(5) = 45x^2 + 14x - 2.

Front

What is the derivative of y = x^2(-3x^2 - 2)?

Back

dy/dx = 2x(-3x^2 - 2) + x^2(-6x) = -12x^3 - 4x.

Front

How do you apply the Product Rule in differentiation?

Back

Identify the two functions being multiplied, differentiate each function separately, and then apply the Product Rule formula.

Front

What is the significance of the derivative in calculus?

Back

The derivative represents the rate of change of a function with respect to its variable, indicating how the function behaves.

Front

What is the first step in using the Product Rule?

Back

Identify the two functions that are being multiplied and differentiate each one.

Front

What does the notation dy/dx represent?

Back

dy/dx represents the derivative of y with respect to x, indicating the slope of the tangent line to the curve at any point.