What is the derivative of (x^2+1sqrt(x)) ?

The derivative of (x^2+1sqrt(x)) is (5x^2+1)/(2sqrt(x))

What is the first derivative of (x^2+1sqrt(x)) ?

The first derivative of (x^2+1sqrt(x)) is (5x^2+1)/(2sqrt(x))

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + 1, g = x

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

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

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

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

Simplify

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

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

What is the derivative of (x^2+1sqrt(x)) ?
The derivative of (x^2+1sqrt(x)) is (5x^2+1)/(2sqrt(x))
What is the first derivative of (x^2+1sqrt(x)) ?
The first derivative of (x^2+1sqrt(x)) is (5x^2+1)/(2sqrt(x))