What is the derivative of y=2x^2log_{e}(x)-x^2 ?

The derivative of y=2x^2log_{e}(x)-x^2 is 4xln(x)

What is the first derivative of y=2x^2log_{e}(x)-x^2 ?

The first derivative of y=2x^2log_{e}(x)-x^2 is 4xln(x)

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derivative of

y = 2 x^{2} lo g_{e} (x) - x^{2}

4 x ln (x)

Solution steps

\frac{d}{d x} (2 x^{2} lo g_{e} (x) - x^{2})

Simplify

2 x^{2} lo g_{e} (x) - x^{2} : 2 x^{2} ln (x) - x^{2}

= \frac{d}{d x} (2 x^{2} ln (x) - x^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x^{2} ln (x)) - \frac{d}{d x} (x^{2})

\frac{d}{d x} (2 x^{2} ln (x)) = 2 (2 x ln (x) + x)

\frac{d}{d x} (x^{2}) = 2 x

= 2 (2 x ln (x) + x) - 2 x

Simplify

2 (2 x ln (x) + x) - 2 x : 4 x ln (x)

= 4 x ln (x)

What is the derivative of y=2x^2log_{e}(x)-x^2 ?
The derivative of y=2x^2log_{e}(x)-x^2 is 4xln(x)
What is the first derivative of y=2x^2log_{e}(x)-x^2 ?
The first derivative of y=2x^2log_{e}(x)-x^2 is 4xln(x)