What is the derivative of (c(200+(50)/x+(x^2)/5)) ?

The derivative of (c(200+(50)/x+(x^2)/5)) is c((2x)/5-(50)/(x^2))

What is the first derivative of (c(200+(50)/x+(x^2)/5)) ?

The first derivative of (c(200+(50)/x+(x^2)/5)) is c((2x)/5-(50)/(x^2))

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\frac{d}{d x} ((c) (200 + \frac{50}{x} + \frac{x ^{2}}{5}))

c (\frac{2 x}{5} - \frac{50}{x ^{2}})

Solution steps

\frac{d}{d x} ((c) (200 + \frac{50}{x} + \frac{x ^{2}}{5}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= c \frac{d}{d x} (200 + \frac{50}{x} + \frac{x ^{2}}{5})

Apply the Sum/Difference Rule:

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

= c (\frac{d}{d x} (200) + \frac{d}{d x} (\frac{50}{x}) + \frac{d}{d x} (\frac{x ^{2}}{5}))

\frac{d}{d x} (200) = 0

\frac{d}{d x} (\frac{50}{x}) = - \frac{50}{x ^{2}}

\frac{d}{d x} (\frac{x ^{2}}{5}) = \frac{2 x}{5}

= c (0 - \frac{50}{x ^{2}} + \frac{2 x}{5})

Simplify

= c (\frac{2 x}{5} - \frac{50}{x ^{2}})

- \frac{1}{5} (2 x^{2} + x - 12)^{5} + C

\frac{( 4 x ^{4} + 9 x ^{3} + 42 x ^{2} + 51 x + 36 )}{3 x ( x ^{2} + 6 ) ^{2}}

\frac{d}{d t} ((x) (x - 1) (1 - 2 x))

3^{(- x - 1)}

(\frac{197}{193} - 0.25 (\frac{394}{193})) \cdot 1 0^{3}

What is the derivative of (c(200+(50)/x+(x^2)/5)) ?
The derivative of (c(200+(50)/x+(x^2)/5)) is c((2x)/5-(50)/(x^2))
What is the first derivative of (c(200+(50)/x+(x^2)/5)) ?
The first derivative of (c(200+(50)/x+(x^2)/5)) is c((2x)/5-(50)/(x^2))