What is the derivative of (2sqrt(x)-1/(5-4sqrt(x))) ?

The derivative of (2sqrt(x)-1/(5-4sqrt(x))) is 3/(sqrt(x)(5-4\sqrt{x))^2}

What is the first derivative of (2sqrt(x)-1/(5-4sqrt(x))) ?

The first derivative of (2sqrt(x)-1/(5-4sqrt(x))) is 3/(sqrt(x)(5-4\sqrt{x))^2}

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\frac{d}{d x} (\frac{2 x - 1}{5 - 4 x})

\frac{3}{x ( 5 - 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x - 1}{5 - 4 x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 2 x - 1 ) ( 5 - 4 x ) - \frac{d}{d x} ( 5 - 4 x ) ( 2 x - 1 )}{( 5 - 4 x ) ^{2}}

\frac{d}{d x} (2 x - 1) = \frac{1}{x}

\frac{d}{d x} (5 - 4 x) = - \frac{2}{x}

= \frac{\frac{1}{x} ( 5 - 4 x ) - ( - \frac{2}{x} ) ( 2 x - 1 )}{( 5 - 4 x ) ^{2}}

Simplify

\frac{\frac{1}{x} ( 5 - 4 x ) - ( - \frac{2}{x} ) ( 2 x - 1 )}{( 5 - 4 x ) ^{2}} : \frac{3}{x ( 5 - 4 x ) ^{2}}

= \frac{3}{x ( 5 - 4 x ) ^{2}}

(\frac{22.2 sin ( 5 t )}{t}) + 44

\int 7 cos (t) d t

n = 3 \sum \infty \frac{1}{4 ^{n}}

4 y^{^{''}} + 8 y^{^{'}} + 13 y = 8 sin (1.5 t)

\int \frac{1}{5 x ^{3}} d x

What is the derivative of (2sqrt(x)-1/(5-4sqrt(x))) ?
The derivative of (2sqrt(x)-1/(5-4sqrt(x))) is 3/(sqrt(x)(5-4\sqrt{x))^2}
What is the first derivative of (2sqrt(x)-1/(5-4sqrt(x))) ?
The first derivative of (2sqrt(x)-1/(5-4sqrt(x))) is 3/(sqrt(x)(5-4\sqrt{x))^2}