Derivatives of Algebraic Functions STEM 1-2BP

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero.

Front

What is the Constant Rule in differentiation?

Back

The Constant Rule states that if \( y = c \) (where c is a constant), then \( \frac{dy}{dx} = 0 \).

Front

What does the Product Rule state?

Back

The Product Rule states that the derivative of the product of two differentiable functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

Front

What does the derivative represent in terms of a graph?

Back

The derivative represents the slope of the tangent line to the graph of the function at a given point.

Front

Differentiate the function \( f(x) = (6x^2 - 7)(5x - 8) \).

Back

The derivative is \( f'(x) = 90x^2 - 96x - 35 \).

Front

What is the Power Rule in differentiation?

Back

The Power Rule states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \).

Front

What is the Chain Rule in differentiation?

Back

The Chain Rule states that if a function is composed of two functions, then the derivative is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.

Front

What is the difference between the slope of the tangent line and the slope of the secant line?

Back

The slope of the tangent line represents the instantaneous rate of change at a point, while the slope of the secant line represents the average rate of change over an interval.

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 Quotient Rule in differentiation?

Back

The Quotient Rule states that if \( f(x) = \frac{g(x)}{h(x)} \), then \( f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2} \).