Another differentiation question

• chaosblack
In summary, differentiation is a mathematical process used to find the rate of change of a quantity over time. It is different from integration, which finds the total change over a given interval. The basic rules of differentiation include the power, product, quotient, and chain rules. It is used in real-life applications to analyze and understand changes in quantities, but it has limitations such as being unable to be applied to all types of functions and not providing information at specific points.
chaosblack

Homework Statement

Supposed "f" is a differentiable function. Write the expression for the derivative of the following function.

a) h(x) = -4x^3 * f(x)

b) h(x) = 2/$$\sqrt{x}$$* f(x)

N/a

The Attempt at a Solution

Would the answers just be (using the product rule)

a) h'(x) = -4x^3 * f '(x) + f(x) * -12x^2

and

b) h'(x) = 2/$$\sqrt{x}$$ * f '(x) + f(x) * -x^-2

Sort of seems to simple... Thanks again

a) Yes, b) $$\frac{2}{\sqrt{x}}$$ is not $$\frac{-1}{x^2}$$

Last edited:

1. What is differentiation?

Differentiation is a mathematical process used to find the rate at which a quantity changes over time. It is a fundamental concept in calculus and is commonly used in physics, engineering, and economics.

2. How is differentiation different from integration?

Integration is the reverse process of differentiation. While differentiation finds the rate of change of a quantity, integration finds the total change over a given interval. They are inverse operations and are used in various applications to solve problems involving rates of change and accumulation.

3. What are the basic rules of differentiation?

The basic rules of differentiation include the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of various functions by following a set of mathematical operations based on the given function.

4. What is the purpose of differentiation in real-life applications?

Differentiation is used in real-life applications to analyze and understand how quantities change over time or in relation to other variables. It is used to solve various problems in science, engineering, and economics, such as finding optimal solutions, predicting future trends, and determining rates of change.

5. What are the limitations of differentiation?

While differentiation is a powerful tool in mathematics and its applications, it does have its limitations. It cannot be applied to all types of functions, such as discontinuous or non-differentiable functions. It also does not provide information about the behavior of a function at specific points, only its overall rate of change.

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