What is the derivative of (3(7-x)+5sqrt(9+x^2))/(15) ?

The derivative of (3(7-x)+5sqrt(9+x^2))/(15) is 1/15 (-3+(5x)/(sqrt(9+x^2)))

What is the first derivative of (3(7-x)+5sqrt(9+x^2))/(15) ?

The first derivative of (3(7-x)+5sqrt(9+x^2))/(15) is 1/15 (-3+(5x)/(sqrt(9+x^2)))

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derivative of

\frac{3 ( 7 - x ) + 5 9 + x ^{2}}{15}

\frac{1}{15} (- 3 + \frac{5 x}{9 + x ^{2}})

Solution steps

\frac{d}{d x} (\frac{3 ( 7 - x ) + 5 9 + x ^{2}}{15})

Take the constant out:

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

= \frac{1}{15} \frac{d}{d x} (3 (7 - x) + 5 9 + x^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{15} (\frac{d}{d x} (3 (7 - x)) + \frac{d}{d x} (5 9 + x^{2}))

\frac{d}{d x} (3 (7 - x)) = - 3

\frac{d}{d x} (5 9 + x^{2}) = \frac{5 x}{9 + x ^{2}}

= \frac{1}{15} (- 3 + \frac{5 x}{9 + x ^{2}})

What is the derivative of (3(7-x)+5sqrt(9+x^2))/(15) ?
The derivative of (3(7-x)+5sqrt(9+x^2))/(15) is 1/15 (-3+(5x)/(sqrt(9+x^2)))
What is the first derivative of (3(7-x)+5sqrt(9+x^2))/(15) ?
The first derivative of (3(7-x)+5sqrt(9+x^2))/(15) is 1/15 (-3+(5x)/(sqrt(9+x^2)))