What is the derivative of xsqrt(169-x^2) ?

The derivative of xsqrt(169-x^2) is (-2x^2+169)/(sqrt(169-x^2))

What is the first derivative of xsqrt(169-x^2) ?

The first derivative of xsqrt(169-x^2) is (-2x^2+169)/(sqrt(169-x^2))

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derivative of

x 169 - x^{2}

\frac{- 2 x ^{2} + 169}{169 - x ^{2}}

Solution steps

\frac{d}{d x} (x 169 - x^{2})

Apply the Product Rule:

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

f = x, g = 169 - x^{2}

= \frac{d x}{d x} 169 - x^{2} + \frac{d}{d x} (169 - x^{2}) x

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

\frac{d}{d x} (169 - x^{2}) = - \frac{x}{169 - x ^{2}}

= 1 \cdot 169 - x^{2} + (- \frac{x}{169 - x ^{2}}) x

Simplify

1 \cdot 169 - x^{2} + (- \frac{x}{169 - x ^{2}}) x : \frac{- 2 x ^{2} + 169}{169 - x ^{2}}

= \frac{- 2 x ^{2} + 169}{169 - x ^{2}}

\int \frac{x}{4 x ^{2} - 1} d x

ln ∣ ln (7 x) ∣

\int_{0}^{4} \frac{5}{3 x + 1} d x

3^{x}

y^{^{'}} = - \frac{y}{x} + \frac{e ^{x}}{x}

What is the derivative of xsqrt(169-x^2) ?
The derivative of xsqrt(169-x^2) is (-2x^2+169)/(sqrt(169-x^2))
What is the first derivative of xsqrt(169-x^2) ?
The first derivative of xsqrt(169-x^2) is (-2x^2+169)/(sqrt(169-x^2))