What is the derivative of f(x)=xsqrt(x^2+21) ?

The derivative of f(x)=xsqrt(x^2+21) is (2x^2+21)/(sqrt(x^2+21))

What is the first derivative of f(x)=xsqrt(x^2+21) ?

The first derivative of f(x)=xsqrt(x^2+21) is (2x^2+21)/(sqrt(x^2+21))

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derivative of

f (x) = x x^{2} + 21

\frac{2 x ^{2} + 21}{x ^{2} + 21}

Solution steps

\frac{d}{d x} (x x^{2} + 21)

Apply the Product Rule:

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

f = x, g = x^{2} + 21

= \frac{d x}{d x} x^{2} + 21 + \frac{d}{d x} (x^{2} + 21) x

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} + 21) = \frac{x}{x ^{2} + 21}

= 1 \cdot x^{2} + 21 + \frac{x}{x ^{2} + 21} x

Simplify

1 \cdot x^{2} + 21 + \frac{x}{x ^{2} + 21} x : \frac{2 x ^{2} + 21}{x ^{2} + 21}

= \frac{2 x ^{2} + 21}{x ^{2} + 21}

x \to \infty lim (1 + 4 x)

x^{2} \frac{d y}{d x} - x y + 1 = 0

x \to \infty lim (- \frac{x}{x})

\int_{0}^{3} 2 e^{x} d x

\frac{d}{d x} (ln (x) - \frac{x ^{2}}{8})

What is the derivative of f(x)=xsqrt(x^2+21) ?
The derivative of f(x)=xsqrt(x^2+21) is (2x^2+21)/(sqrt(x^2+21))
What is the first derivative of f(x)=xsqrt(x^2+21) ?
The first derivative of f(x)=xsqrt(x^2+21) is (2x^2+21)/(sqrt(x^2+21))