What is the derivative of ((x^2+1(x+3)^{1/2})/(x-1)) ?

The derivative of ((x^2+1(x+3)^{1/2})/(x-1)) is (3x^3+x^2-13x-7)/(2(x-1)^2(x+3)^{1/2)}

What is the first derivative of ((x^2+1(x+3)^{1/2})/(x-1)) ?

The first derivative of ((x^2+1(x+3)^{1/2})/(x-1)) is (3x^3+x^2-13x-7)/(2(x-1)^2(x+3)^{1/2)}

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

\frac{3 x ^{3} + x ^{2} - 13 x - 7}{2 ( x - 1 ) ^{2} ( x + 3 ) ^{\frac{1}{2}}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((x^{2} + 1) (x + 3)^{\frac{1}{2}}) = \frac{5 x ^{2} + 12 x + 1}{2 ( x + 3 ) ^{\frac{1}{2}}}

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

= \frac{\frac{5 x ^{2} + 12 x + 1}{2 ( x + 3 ) ^{\frac{1}{2}}} ( x - 1 ) - 1 \cdot ( x ^{2} + 1 ) ( x + 3 ) ^{\frac{1}{2}}}{( x - 1 ) ^{2}}

Simplify

\frac{\frac{5 x ^{2} + 12 x + 1}{2 ( x + 3 ) ^{\frac{1}{2}}} ( x - 1 ) - 1 \cdot ( x ^{2} + 1 ) ( x + 3 ) ^{\frac{1}{2}}}{( x - 1 ) ^{2}} : \frac{3 x ^{3} + x ^{2} - 13 x - 7}{2 ( x - 1 ) ^{2} ( x + 3 ) ^{\frac{1}{2}}}

= \frac{3 x ^{3} + x ^{2} - 13 x - 7}{2 ( x - 1 ) ^{2} ( x + 3 ) ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{x + 5}{x - 5})

y^{^{'}} (x^{2} + 1) + 5 x (y - 1) = 0, y (0) = 7

x \to 0 lim (\frac{sin ( x )}{2})

\int x^{4} \cdot e^{x^{5} + 2} d x

5^{s i n (2 x)}

What is the derivative of ((x^2+1(x+3)^{1/2})/(x-1)) ?
The derivative of ((x^2+1(x+3)^{1/2})/(x-1)) is (3x^3+x^2-13x-7)/(2(x-1)^2(x+3)^{1/2)}
What is the first derivative of ((x^2+1(x+3)^{1/2})/(x-1)) ?
The first derivative of ((x^2+1(x+3)^{1/2})/(x-1)) is (3x^3+x^2-13x-7)/(2(x-1)^2(x+3)^{1/2)}