What is the slope of y=-5x^{1/2}+x^{3/2} ?

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

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slope of y=-5x^{1/2}+x^{3/2}

slope

y = - 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}

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

Solution steps

y = - 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}

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

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

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

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

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

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

\int \frac{2}{3} x^{\frac{3}{2}} - 6 sin (x) + C d x

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

\int \frac{1}{289 + x ^{2}} d x

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