What is the derivative of (f(5x))^2-2 ?

The derivative of (f(5x))^2-2 is 50fx^2

What is the first derivative of (f(5x))^2-2 ?

The first derivative of (f(5x))^2-2 is 50fx^2

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derivative of

(f (5 x))^{2} - 2

50 f x^{2}

Solution steps

\frac{d}{df} ((f \cdot 5 x)^{2} - 2)

Simplify

(f \cdot 5 x)^{2} - 2 : 25 f^{2} x^{2} - 2

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{d}{df} (25 f^{2} x^{2}) = 50 x^{2} f

\frac{d}{df} (2) = 0

= 50 x^{2} f - 0

Simplify

= 50 f x^{2}

What is the derivative of (f(5x))^2-2 ?
The derivative of (f(5x))^2-2 is 50fx^2
What is the first derivative of (f(5x))^2-2 ?
The first derivative of (f(5x))^2-2 is 50fx^2