Exercise
Find the derivative of the following function:
f ( x ) = x 2 ln x + 1 f(x)=\frac{x^2}{\ln x+1} f ( x ) = ln x + 1 x 2
Final Answer
Show final answer
f'(x)=\frac{2x\ln x +x}{{(\ln x+1)}^2}
Solution
f ( x ) = x 2 ln x + 1 f(x)=\frac{x^2}{\ln x+1} f ( x ) = ln x + 1 x 2
Using Derivative formulas Derivative Rules
f ′ ( x ) = 2 x ( ln x + 1 ) − x 2 ⋅ 1 x ( ln x + 1 ) 2 = f'(x)=\frac{2x(\ln x +1)-x^2\cdot\frac{1}{x}}{{(\ln x+1)}^2}= f ′ ( x ) = ( ln x + 1 ) 2 2 x ( ln x + 1 ) − x 2 ⋅ x 1 =
One can simplify the derivative:
= 2 x ln x + 2 x − x ( ln x + 1 ) 2 = =\frac{2x\ln x +2x-x}{{(\ln x+1)}^2}= = ( ln x + 1 ) 2 2 x ln x + 2 x − x =
= 2 x ln x + x ( ln x + 1 ) 2 =\frac{2x\ln x +x}{{(\ln x+1)}^2} = ( ln x + 1 ) 2 2 x ln x + x
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