What is the derivative of 8x+sqrt(x^2+7x+3) ?

The derivative of 8x+sqrt(x^2+7x+3) is 8+(2x+7)/(2sqrt(x^2+7x+3))

What is the first derivative of 8x+sqrt(x^2+7x+3) ?

The first derivative of 8x+sqrt(x^2+7x+3) is 8+(2x+7)/(2sqrt(x^2+7x+3))

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\frac{d}{d x} (8 x + x^{2} + 7 x + 3)

8 + \frac{2 x + 7}{2 x ^{2} + 7 x + 3}

Solution steps

\frac{d}{d x} (8 x + x^{2} + 7 x + 3)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (8 x) + \frac{d}{d x} (x^{2} + 7 x + 3)

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

\frac{d}{d x} (x^{2} + 7 x + 3) = \frac{2 x + 7}{2 x ^{2} + 7 x + 3}

= 8 + \frac{2 x + 7}{2 x ^{2} + 7 x + 3}

What is the derivative of 8x+sqrt(x^2+7x+3) ?
The derivative of 8x+sqrt(x^2+7x+3) is 8+(2x+7)/(2sqrt(x^2+7x+3))
What is the first derivative of 8x+sqrt(x^2+7x+3) ?
The first derivative of 8x+sqrt(x^2+7x+3) is 8+(2x+7)/(2sqrt(x^2+7x+3))