What is the derivative of xsqrt(a^2+x^2) ?

The derivative of xsqrt(a^2+x^2) is (2x^2+a^2)/(sqrt(a^2+x^2))

What is the first derivative of xsqrt(a^2+x^2) ?

The first derivative of xsqrt(a^2+x^2) is (2x^2+a^2)/(sqrt(a^2+x^2))

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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