What is the derivative of (10x+x^2)/2 ?

The derivative of (10x+x^2)/2 is 5+x

What is the first derivative of (10x+x^2)/2 ?

The first derivative of (10x+x^2)/2 is 5+x

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derivative of

\frac{10 x + x ^{2}}{2}

5 + x

Solution steps

\frac{d}{d x} (\frac{10 x + x ^{2}}{2})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (10 x + x^{2})

Apply the Sum/Difference Rule:

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

= \frac{1}{2} (\frac{d}{d x} (10 x) + \frac{d}{d x} (x^{2}))

\frac{d}{d x} (10 x) = 10

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

= \frac{1}{2} (10 + 2 x)

Simplify

\frac{1}{2} (10 + 2 x) : 5 + x

= 5 + x

What is the derivative of (10x+x^2)/2 ?
The derivative of (10x+x^2)/2 is 5+x
What is the first derivative of (10x+x^2)/2 ?
The first derivative of (10x+x^2)/2 is 5+x