What is the derivative of y=sqrt(x)+x^{3/2}-8x ?

The derivative of y=sqrt(x)+x^{3/2}-8x is 1/(2x^{1/2)}+(3x^{1/2})/2-8

What is the first derivative of y=sqrt(x)+x^{3/2}-8x ?

The first derivative of y=sqrt(x)+x^{3/2}-8x is 1/(2x^{1/2)}+(3x^{1/2})/2-8

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derivative of

y = x + x^{\frac{3}{2}} - 8 x

\frac{1}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2} - 8

Solution steps

\frac{d}{d x} (x + x^{\frac{3}{2}} - 8 x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x) + \frac{d}{d x} (x^{\frac{3}{2}}) - \frac{d}{d x} (8 x)

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

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

\frac{d}{d x} (8 x) = 8

= \frac{1}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2} - 8

(5 x^{3} + 3 x y + 2 y^{2}) d x + (x^{2} + 2 x y) d y = 0

\frac{d}{d x} (ln (x^{2} + 2 x))

x \to 0 lim (ln (2 x^{2} + x))

\int \frac{x}{x ^{2} + 49} d x

\frac{1}{( s - 3 ) ( s - 9 )}

What is the derivative of y=sqrt(x)+x^{3/2}-8x ?
The derivative of y=sqrt(x)+x^{3/2}-8x is 1/(2x^{1/2)}+(3x^{1/2})/2-8
What is the first derivative of y=sqrt(x)+x^{3/2}-8x ?
The first derivative of y=sqrt(x)+x^{3/2}-8x is 1/(2x^{1/2)}+(3x^{1/2})/2-8