What is the derivative of f(x)=9ln(9+2x^2) ?

The derivative of f(x)=9ln(9+2x^2) is (36x)/(9+2x^2)

What is the first derivative of f(x)=9ln(9+2x^2) ?

The first derivative of f(x)=9ln(9+2x^2) is (36x)/(9+2x^2)

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derivative of

f (x) = 9 ln (9 + 2 x^{2})

\frac{36 x}{9 + 2 x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{9 + 2 x ^{2}} \frac{d}{d x} (9 + 2 x^{2})

= \frac{1}{9 + 2 x ^{2}} \frac{d}{d x} (9 + 2 x^{2})

\frac{d}{d x} (9 + 2 x^{2}) = 4 x

= 9 \cdot \frac{1}{9 + 2 x ^{2}} \cdot 4 x

Simplify

9 \cdot \frac{1}{9 + 2 x ^{2}} \cdot 4 x : \frac{36 x}{9 + 2 x ^{2}}

= \frac{36 x}{9 + 2 x ^{2}}

What is the derivative of f(x)=9ln(9+2x^2) ?
The derivative of f(x)=9ln(9+2x^2) is (36x)/(9+2x^2)
What is the first derivative of f(x)=9ln(9+2x^2) ?
The first derivative of f(x)=9ln(9+2x^2) is (36x)/(9+2x^2)