Differentiation

Front

What is the derivative of y=5x^4?

Back

20x^3

Front

Find the derivative of f(x) = x^3 + x^2 + 3.

Back

3x^2 + 2x

Front

If the position function for a particle is s(t) = -t^2 - t, what is the expression for the instantaneous velocity?

Back

v(t) = -2t - 1

Front

Find the derivative of f(x) = 6x^30 - 2x^15 + 4x^3 - 2x + 1.

Back

f'(x) = 180x^29 - 30x^14 + 12x^2 - 2

Front

What is the derivative of y=3x^2 - 4x + 2?

Back

6x - 4

Front

Define differentiation in calculus.

Back

Differentiation is the process of finding the derivative of a function, which represents the rate of change of the function with respect to a variable.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What does the derivative represent in a real-world context?

Back

The derivative represents the rate of change or the slope of a function at a given point, often interpreted as velocity in motion problems.

Front

How do you differentiate a constant function?

Back

The derivative of a constant function is zero.

Front

What is the sum rule in differentiation?

Back

The sum rule states that the derivative of a sum of functions is the sum of their derivatives: (f + g)' = f' + g'.