In Exercises 41–64, find the derivative of the function. g(t)=(lnt)/(t^2)

Name: Problem 53, Chapter 5: Calculus of a Single Variable
Uploaded: 2021-02-24T13:17:38-08:00
Duration: 5 min 5 s
Channel: Anurag Kumar
Description: In Exercises 41–64, find the derivative of the function. g(t)=(lnt)/(t^2)

step 1 function G of t equal to natural log t upon t square so we have to find the derivative of this f

In Exercises 41–64, find the derivative of the function....

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Key Concepts

Quotient Rule

The quotient rule is a fundamental technique in differential calculus used to differentiate functions that are expressed as one function divided by another. It involves taking the derivative of the numerator and the denominator separately, then combining these derivatives in a specific formula to obtain the overall derivative.

Power Rule

The power rule is a basic differentiation technique used for functions of the form t^n, where it allows one to quickly determine the derivative by multiplying by the exponent and reducing the exponent by one. This rule is essential when differentiating polynomial functions or any function that can be expressed with constant exponents.

Derivative of the Natural Logarithm Function

In calculus, the derivative of the natural logarithm function ln(t) is a fundamental result that states the derivative is 1/t (for t > 0). This rule is frequently used in combination with other differentiation rules when logarithmic functions are involved.

Algebraic Simplification

After applying differentiation techniques such as the quotient rule, power rule, or chain rule, it is often necessary to perform algebraic simplification. This step involves combining like terms and simplifying expressions to achieve a more compact or interpretable final derivative form.

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