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Differential Calculus

At its simplest it is a method of finding the gradient of a tangent to a curve. The gradient of the tangent is a measure of how quickly the function is changing as the x-coordinate changes.

Where is it used?

All things move, for example, the hands on a clock, the sprinter in a

100m race, the molecules in a chemical reaction, the share values

on the stock market. Mathematics can be used to model all of these

situations. Since each situation is dynamic, the models will involve

differential calculus.

Feel free to watch this video and discover why calculus is so amazing!! I would highly recommend watching the first 3 and a half minutes at least.

We will be learning both versions of calculus, differential calculus and integral calculus, that are described in this video.

Differentiation is a method used to find the equation of the gradient fucntion for a given function, y = f(x)

To differentiate a function, find the gradient function:

The process is valid for all values of n, both positive and negative, and fractions or decimals.

1

Differentiate, use proper notation in your answer

1

Differentiate, use proper notation in your answer

1

Differentiate, use proper notation in your answer

1

Differentiate, use proper notation in your answer

1

Find f'(x), use proper notation in your answer

1

Find f'(x), use proper notation in your answer

1

Find f'(x), use proper notation in your answer

1

Find f'(x), use proper notation in your answer

Changing the variable changes the notation, but not the procces.

1

Differentiate the following with respect to x. Use correct notation for your answer and answer using positive exponents.

1

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

1

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

1

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

1

Find dA/dt

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Power Rule (Introduction into Differential Calculus)

Power Rule (Introduction into Differential Calculus)

Differentiate, use proper notation in your answer

Differentiate, use proper notation in your answer

Differentiate, use proper notation in your answer

Differentiate, use proper notation in your answer

Find f'(x), use proper notation in your answer

Find f'(x), use proper notation in your answer

Find f'(x), use proper notation in your answer

Find f'(x), use proper notation in your answer

Differentiate the following with respect to x. Use correct notation for your answer and answer using positive exponents.

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

Find dA/dt

Find dA/dt

Differentiate, use proper notation in your answer

Differentiate, use proper notation in your answer

Differentiate, use proper notation in your answer

Differentiate, use proper notation in your answer

Find f'(x), use proper notation in your answer

Find f'(x), use proper notation in your answer

Find f'(x), use proper notation in your answer

Find f'(x), use proper notation in your answer

Differentiate the following with respect to x. Use correct notation for your answer and answer using positive exponents.

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

Differentiate the following with respect to x. Use correct notation for your answerand answer using positive exponents.

Find dA/dt

Find dA/dt