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

The derivative of sqrt(x^2+(1/2 x-5)^2) is (5(x-2))/(2sqrt(5x^2-20x+100))

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

The first derivative of sqrt(x^2+(1/2 x-5)^2) is (5(x-2))/(2sqrt(5x^2-20x+100))

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derivative of

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

\frac{5 ( x - 2 )}{2 5 x ^{2} - 20 x + 100}

Solution steps

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

Apply the chain rule:

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

= \frac{1}{2 x ^{2} + ( \frac{1}{2} x - 5 ) ^{2}} \frac{d}{d x} (x^{2} + (\frac{1}{2} x - 5)^{2})

\frac{d}{d x} (x^{2} + (\frac{1}{2} x - 5)^{2}) = \frac{5 ( x - 2 )}{2}

= \frac{1}{2 x ^{2} + ( \frac{1}{2} x - 5 ) ^{2}} \cdot \frac{5 ( x - 2 )}{2}

Simplify

\frac{1}{2 x ^{2} + ( \frac{1}{2} x - 5 ) ^{2}} \cdot \frac{5 ( x - 2 )}{2} : \frac{5 ( x - 2 )}{2 5 x ^{2} - 20 x + 100}

= \frac{5 ( x - 2 )}{2 5 x ^{2} - 20 x + 100}

f (x) = 6 x sin (x)

\frac{d y}{d x} = x x - 9

y = 3 - x, y = - 3 - x, y = x - 1

x \to 1 lim (4 x^{2} - 7 x + 5)

What is the derivative of sqrt(x^2+(1/2 x-5)^2) ?
The derivative of sqrt(x^2+(1/2 x-5)^2) is (5(x-2))/(2sqrt(5x^2-20x+100))
What is the first derivative of sqrt(x^2+(1/2 x-5)^2) ?
The first derivative of sqrt(x^2+(1/2 x-5)^2) is (5(x-2))/(2sqrt(5x^2-20x+100))