What is the derivative of (-5/2 /(x^2)+5^x) ?

The derivative of (-5/2 /(x^2)+5^x) is 5/(x^3)+ln(5)*5^x

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

The first derivative of (-5/2 /(x^2)+5^x) is 5/(x^3)+ln(5)*5^x

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

\frac{5}{x ^{3}} + ln (5) \cdot 5^{x}

Solution steps

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

Simplify

\frac{- \frac{5}{2}}{x ^{2}} + 5^{x} : - \frac{5}{2 x ^{2}} + 5^{x}

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

Apply the Sum/Difference Rule:

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

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

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

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

= - (- \frac{5}{x ^{3}}) + 5^{x} ln (5)

Simplify

= \frac{5}{x ^{3}} + ln (5) \cdot 5^{x}

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

\frac{d}{d x} (e^{c o s (\frac{1}{x})})

\int \frac{6400 x}{16 x ^{2} + 3200} d x

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

x \to 0 lim (x^{6 s i n (x)})

What is the derivative of (-5/2 /(x^2)+5^x) ?
The derivative of (-5/2 /(x^2)+5^x) is 5/(x^3)+ln(5)*5^x
What is the first derivative of (-5/2 /(x^2)+5^x) ?
The first derivative of (-5/2 /(x^2)+5^x) is 5/(x^3)+ln(5)*5^x