What is the derivative of y=(2log_{e}(x)-3)^4 ?

The derivative of y=(2log_{e}(x)-3)^4 is (8(2ln(x)-3)^3)/x

What is the first derivative of y=(2log_{e}(x)-3)^4 ?

The first derivative of y=(2log_{e}(x)-3)^4 is (8(2ln(x)-3)^3)/x

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derivative of

y = (2 lo g_{e} (x) - 3)^{4}

\frac{8 ( 2 ln ( x ) - 3 ) ^{3}}{x}

Solution steps

\frac{d}{d x} ((2 lo g_{e} (x) - 3)^{4})

Simplify

(2 lo g_{e} (x) - 3)^{4} : (2 ln (x) - 3)^{4}

= \frac{d}{d x} ((2 ln (x) - 3)^{4})

Apply the chain rule:

4 (2 ln (x) - 3)^{3} \frac{d}{d x} (2 ln (x) - 3)

= 4 (2 ln (x) - 3)^{3} \frac{d}{d x} (2 ln (x) - 3)

\frac{d}{d x} (2 ln (x) - 3) = \frac{2}{x}

= 4 (2 ln (x) - 3)^{3} \frac{2}{x}

Simplify

4 (2 ln (x) - 3)^{3} \frac{2}{x} : \frac{8 ( 2 ln ( x ) - 3 ) ^{3}}{x}

= \frac{8 ( 2 ln ( x ) - 3 ) ^{3}}{x}

What is the derivative of y=(2log_{e}(x)-3)^4 ?
The derivative of y=(2log_{e}(x)-3)^4 is (8(2ln(x)-3)^3)/x
What is the first derivative of y=(2log_{e}(x)-3)^4 ?
The first derivative of y=(2log_{e}(x)-3)^4 is (8(2ln(x)-3)^3)/x