What is the derivative of 1/3 x^{3/2}-x^5+pi^4 ?

The derivative of 1/3 x^{3/2}-x^5+pi^4 is -5x^4+(x^{1/2})/2

What is the first derivative of 1/3 x^{3/2}-x^5+pi^4 ?

The first derivative of 1/3 x^{3/2}-x^5+pi^4 is -5x^4+(x^{1/2})/2

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\frac{d}{d x} (\frac{1}{3} x^{\frac{3}{2}} - x^{5} + π^{4})

- 5 x^{4} + \frac{x ^{\frac{1}{2}}}{2}

Solution steps

\frac{d}{d x} (\frac{1}{3} x^{\frac{3}{2}} - x^{5} + π^{4})

Simplify

\frac{1}{3} x^{\frac{3}{2}} - x^{5} + π^{4} : \frac{x ^{\frac{3}{2}}}{3} - x^{5} + π^{4}

= \frac{d}{d x} (\frac{x ^{\frac{3}{2}}}{3} - x^{5} + π^{4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{\frac{3}{2}}}{3}) - \frac{d}{d x} (x^{5}) + \frac{d}{d x} (π^{4})

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (π^{4}) = 0

= \frac{x ^{\frac{1}{2}}}{2} - 5 x^{4} + 0

Simplify

= - 5 x^{4} + \frac{x ^{\frac{1}{2}}}{2}

\frac{d}{d t} (2 t)

25 y^{^{''}} - y = \frac{x e x}{5}

y^{^{'}} + ln (x) y = ln (x)

\int (sin (x) + cos (x))^{2} d x

\frac{d}{d x} (\frac{x - 3}{6 x - 5})

What is the derivative of 1/3 x^{3/2}-x^5+pi^4 ?
The derivative of 1/3 x^{3/2}-x^5+pi^4 is -5x^4+(x^{1/2})/2
What is the first derivative of 1/3 x^{3/2}-x^5+pi^4 ?
The first derivative of 1/3 x^{3/2}-x^5+pi^4 is -5x^4+(x^{1/2})/2