
What is the differentiation of ?
Answer
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Hint: In the given problem, we are required to differentiate with respect to x. Since, is a composite function, we will have to apply the chain rule of differentiation in the process of differentiating . So, differentiation of with respect to x will be done layer by layer using the chain rule of differentiation. Also derivatives of 2x with respect to x must be remembered in order to solve the given problem.
Complete step by step solution:
So, we have,
Keeping the expression inside the logarithmic function inside the bracket, we get,
Now, Let us assume . So substituting as , we get,
Now, we know that differentiation of logarithmic function with respect to x is . So, we get,
Now, putting back as , we get,
because
Now, we take the constants out of the differentiation. So, we get,
Now, we know that the derivative of x with respect to x is . Hence, we get,
Cancelling the common factors in numerator and denominator, we get,
So, the derivative of with respect to x is .
So, the correct answer is “ ”.
Note: The chain rule of differentiation involves differentiating a composite by introducing new unknowns to ease the process and examine the behaviour of function layer by layer. The derivative of the basic logarithmic function with respect to x is . The power rule of differentiation is as follows: .
Complete step by step solution:
So, we have,
Keeping the expression inside the logarithmic function inside the bracket, we get,
Now, Let us assume
Now, we know that differentiation of logarithmic function
Now, putting back
Now, we take the constants out of the differentiation. So, we get,
Now, we know that the derivative of x with respect to x is
Cancelling the common factors in numerator and denominator, we get,
So, the derivative of
So, the correct answer is “
Note: The chain rule of differentiation involves differentiating a composite by introducing new unknowns to ease the process and examine the behaviour of function layer by layer. The derivative of the basic logarithmic function
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