What is the slope of f(x)=(1+3x^{1/2})/(5+x^{3/2)} ?

The slope of f(x)=(1+3x^{1/2})/(5+x^{3/2)} is (-3x-6x^{3/2}+15)/(2x^{1/2)(5+x^{3/2})^2}

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slope of f(x)=(1+3x^{1/2})/(5+x^{3/2)}

slope

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

\frac{- 3 x - 6 x ^{\frac{3}{2}} + 15}{2 x ^{\frac{1}{2}} ( 5 + x ^{\frac{3}{2}} ) ^{2}}

Solution steps

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

In order to find the slope of the function, take the derivative of

\frac{1 + 3 x ^{\frac{1}{2}}}{5 + x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{1 + 3 x ^{\frac{1}{2}}}{5 + x ^{\frac{3}{2}}}) = \frac{- 3 x - 6 x ^{\frac{3}{2}} + 15}{2 x ^{\frac{1}{2}} ( 5 + x ^{\frac{3}{2}} ) ^{2}}

\frac{- 3 x - 6 x ^{\frac{3}{2}} + 15}{2 x ^{\frac{1}{2}} ( 5 + x ^{\frac{3}{2}} ) ^{2}}

y = 7 x + 4

6 x^{2} cos (x) cot (x)

\int_{1}^{3} x^{3} + 2 x - 3 d x

f (x) = (3 x + 5)^{2}

\int \frac{1}{cos ( x ) + 1} d x

What is the slope of f(x)=(1+3x^{1/2})/(5+x^{3/2)} ?
The slope of f(x)=(1+3x^{1/2})/(5+x^{3/2)} is (-3x-6x^{3/2}+15)/(2x^{1/2)(5+x^{3/2})^2}