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

x \to 9 - lim (x^{2} - 3 x)

\int \frac{( ln ( x ) ) ^{\frac{7}{2}}}{x} d x

\int_{- \infty}^{2} e^{x} d x

x \to 2 lim (x^{3} + x^{2} + 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