Differentiation rules

Choose a differentiation rule that fits the structure and check its conditions.

Meaning

Rules for products, quotients, and compositions calculate the rate of change of a combined expression using the rates of its parts. First identify how the expression is assembled.

Example

For multiply the derivative of the outer square by the derivative of the inner to get The inner value u=3x+1 changes by 3h when x changes by h. The square's difference quotient is ((u+3h)²−u²)/h=6u+9h, tending to 6u. This is the outer rate 2u multiplied by the inner rate 3.Do not omit the inner derivative in a composition. The derivative of a product is not simply the product of the derivatives.

Practice for this concept

Scope and references

Topics

Sum, product, quotient, and chain rules; derivatives of exponential, logarithmic, and trigonometric functions

Learning goal

Choose a differentiation rule that fits the structure and check its conditions.

Helpful background

Review derivatives and structures such as compositions, products, and quotients.

Differentiation methods

These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.

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