What is the derivative of f(x)=3sqrt(25-x^2) ?

The derivative of f(x)=3sqrt(25-x^2) is -(3x)/(sqrt(25-x^2))

What is the first derivative of f(x)=3sqrt(25-x^2) ?

The first derivative of f(x)=3sqrt(25-x^2) is -(3x)/(sqrt(25-x^2))

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derivative of

f (x) = 3 25 - x^{2}

- \frac{3 x}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (3 25 - x^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (25 - x^{2})

Apply the chain rule:

\frac{1}{2 25 - x ^{2}} \frac{d}{d x} (25 - x^{2})

= \frac{1}{2 25 - x ^{2}} \frac{d}{d x} (25 - x^{2})

\frac{d}{d x} (25 - x^{2}) = - 2 x

= 3 \cdot \frac{1}{2 25 - x ^{2}} (- 2 x)

Simplify

3 \cdot \frac{1}{2 25 - x ^{2}} (- 2 x) : - \frac{3 x}{25 - x ^{2}}

= - \frac{3 x}{25 - x ^{2}}

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What is the derivative of f(x)=3sqrt(25-x^2) ?
The derivative of f(x)=3sqrt(25-x^2) is -(3x)/(sqrt(25-x^2))
What is the first derivative of f(x)=3sqrt(25-x^2) ?
The first derivative of f(x)=3sqrt(25-x^2) is -(3x)/(sqrt(25-x^2))