What is the derivative of x/((2x+2*sqrt(x+3))) ?

The derivative of x/((2x+2*sqrt(x+3))) is (x+6)/((2x+2sqrt(x+3))^2\sqrt{x+3)}

What is the first derivative of x/((2x+2*sqrt(x+3))) ?

The first derivative of x/((2x+2*sqrt(x+3))) is (x+6)/((2x+2sqrt(x+3))^2\sqrt{x+3)}

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derivative of

\frac{x}{( 2 x + 2 \cdot x + 3 )}

\frac{x + 6}{( 2 x + 2 x + 3 ) ^{2} x + 3}

Solution steps

\frac{d}{d x} (\frac{x}{2 x + 2 x + 3})

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (2 x + 2 x + 3) = 2 + \frac{1}{x + 3}

= \frac{1 \cdot ( 2 x + 2 x + 3 ) - ( 2 + \frac{1}{x + 3} ) x}{( 2 x + 2 x + 3 ) ^{2}}

Simplify

\frac{1 \cdot ( 2 x + 2 x + 3 ) - ( 2 + \frac{1}{x + 3} ) x}{( 2 x + 2 x + 3 ) ^{2}} : \frac{x + 6}{( 2 x + 2 x + 3 ) ^{2} x + 3}

= \frac{x + 6}{( 2 x + 2 x + 3 ) ^{2} x + 3}

\int_{0}^{5} \frac{1}{x ^{\frac{16}{17}}} d x

\frac{d}{d θ} (5 sin (θ))

x \to 0 lim (\frac{1}{4} (4)^{4})

\int tan (3 t) d t

y^{^{'''}} + y^{^{''}} = x

What is the derivative of x/((2x+2*sqrt(x+3))) ?
The derivative of x/((2x+2*sqrt(x+3))) is (x+6)/((2x+2sqrt(x+3))^2\sqrt{x+3)}
What is the first derivative of x/((2x+2*sqrt(x+3))) ?
The first derivative of x/((2x+2*sqrt(x+3))) is (x+6)/((2x+2sqrt(x+3))^2\sqrt{x+3)}