First 15 U3 Review 1A

Front

What is the derivative of y = e^(5x) + 1?

Back

y' = 5e^(5x)

Front

What is the best method to choose the correct answer in multiple-choice questions?

Back

Evaluate each option based on the question's requirements and eliminate incorrect choices.

Front

Find the derivative of f(x) = (x^6 + 4)^5.

Back

f'(x) = 30x^5(x^6 + 4)^4 using the chain rule.

Front

How do you find dy/dx for y = e^(2x) * sin(x)?

Back

Use the product rule: dy/dx = e^(2x)(cos(x)) + sin(x)(2e^(2x)).

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

What is the product rule in differentiation?

Back

The product rule states that if u and v are functions of x, then d(uv)/dx = u'v + uv'.

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

Front

What is the significance of the exponential function in calculus?

Back

The exponential function e^x has the unique property that its derivative is equal to itself.

Front

How do you differentiate a constant?

Back

The derivative of a constant is zero.

Front

What is the power rule in differentiation?

Back

The power rule states that d(x^n)/dx = n*x^(n-1) for any real number n.