First 15 U3 Review 4A

Front

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

Back

y' = 5e^(5x)

Front

How do you find the derivative of y = e^(2x) * sin(x)?

Back

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

Front

What is the best answer to a multiple-choice question if the options are A, B, C, D and you choose C?

Back

C is the selected answer.

Front

What is the derivative of f(x) = (x^6 + 4)^5?

Back

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

Front

What is the product rule in differentiation?

Back

If u and v are functions of x, then the derivative of their product is: (uv)' = u'v + uv'.

Front

What is the chain rule in differentiation?

Back

If y = f(g(x)), then the derivative is: dy/dx = f'(g(x)) * g'(x).

Front

What is the exponential function and its derivative?

Back

The exponential function is y = e^x, and its derivative is dy/dx = e^x.

Front

What is the significance of the constant 'e' in calculus?

Back

The constant 'e' is the base of natural logarithms and is approximately equal to 2.71828; it is important in growth and decay problems.

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero.

Front

How do you differentiate a power function?

Back

For f(x) = x^n, the derivative is f'(x) = n*x^(n-1).