What is the derivative of (f(6x))^2+3 ?

The derivative of (f(6x))^2+3 is 72fx^2

What is the first derivative of (f(6x))^2+3 ?

The first derivative of (f(6x))^2+3 is 72fx^2

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derivative of

(f (6 x))^{2} + 3

72 f x^{2}

Solution steps

\frac{d}{df} ((f \cdot 6 x)^{2} + 3)

Simplify

(f \cdot 6 x)^{2} + 3 : 36 f^{2} x^{2} + 3

= \frac{d}{df} (36 f^{2} x^{2} + 3)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{df} (36 f^{2} x^{2}) + \frac{d}{df} (3)

\frac{d}{df} (36 f^{2} x^{2}) = 72 x^{2} f

\frac{d}{df} (3) = 0

= 72 x^{2} f + 0

Simplify

= 72 f x^{2}

What is the derivative of (f(6x))^2+3 ?
The derivative of (f(6x))^2+3 is 72fx^2
What is the first derivative of (f(6x))^2+3 ?
The first derivative of (f(6x))^2+3 is 72fx^2