What is the derivative of (2sqrt(x)+1(x^2+3)) ?

The derivative of (2sqrt(x)+1(x^2+3)) is (5x^2+2xsqrt(x)+3)/(sqrt(x))

What is the first derivative of (2sqrt(x)+1(x^2+3)) ?

The first derivative of (2sqrt(x)+1(x^2+3)) is (5x^2+2xsqrt(x)+3)/(sqrt(x))

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\frac{d}{d x} ((2 x + 1) (x^{2} + 3))

\frac{5 x ^{2} + 2 x x + 3}{x}

Solution steps

\frac{d}{d x} ((2 x + 1) (x^{2} + 3))

Apply the Product Rule:

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

f = 2 x + 1, g = x^{2} + 3

= \frac{d}{d x} (2 x + 1) (x^{2} + 3) + \frac{d}{d x} (x^{2} + 3) (2 x + 1)

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

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

= \frac{1}{x} (x^{2} + 3) + 2 x (2 x + 1)

Simplify

\frac{1}{x} (x^{2} + 3) + 2 x (2 x + 1) : \frac{5 x ^{2} + 2 x x + 3}{x}

= \frac{5 x ^{2} + 2 x x + 3}{x}

f (x) = (x - 1)^{3}

x \to - 2 lim (\frac{- x}{x + 2})

x \to π lim (1)

\int tan (x) + cot (x) d x

f (x) = \frac{e ^{5 x}}{2 x - 5}

What is the derivative of (2sqrt(x)+1(x^2+3)) ?
The derivative of (2sqrt(x)+1(x^2+3)) is (5x^2+2xsqrt(x)+3)/(sqrt(x))
What is the first derivative of (2sqrt(x)+1(x^2+3)) ?
The first derivative of (2sqrt(x)+1(x^2+3)) is (5x^2+2xsqrt(x)+3)/(sqrt(x))