
What is the derivative of ?
Answer
445.8k+ views
Hint: In this question, we have to find out the derivative for the given particulars.
We have to differentiate the given function with respect to x. Since it is a composite function we need to use chain rule and applying the differentiation formula, we will get the required result.
Formula:
Chain Rule:
If a function f is a function of g then the derivative of the function is denoted by and the chain rule states that: .
Differentiation formula:
Complete step-by-step solution:
We need to find out the derivative of ,
i.e. .
Differentiating using the chain rule which states that: where,
We get,
[Using the formula, ]
[Using the formula, ]
Note: The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Derivative of a function can be written as or .
Composite function:
A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, is the composite function of f and .
is the irrational number called the Euler's number. It’s probably the second most commonly known irrational number after . Its value is and it goes on.
The is an exponent indicating how many times to multiply e by itself. The is a variable. If is , that means . If x is , that means .
We have to differentiate the given function with respect to x. Since it is a composite function we need to use chain rule and applying the differentiation formula, we will get the required result.
Formula:
Chain Rule:
If a function f is a function of g then the derivative of the function
Differentiation formula:
Complete step-by-step solution:
We need to find out the derivative of
i.e.
Differentiating
We get,
Note: The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Derivative of a function
Composite function:
A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example,
The
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