What is the derivative of (f(4x))^2+5 ?

The derivative of (f(4x))^2+5 is 32fx^2

What is the first derivative of (f(4x))^2+5 ?

The first derivative of (f(4x))^2+5 is 32fx^2

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derivative of

(f (4 x))^{2} + 5

32 f x^{2}

Solution steps

\frac{d}{df} ((f \cdot 4 x)^{2} + 5)

Simplify

(f \cdot 4 x)^{2} + 5 : 16 f^{2} x^{2} + 5

= \frac{d}{df} (16 f^{2} x^{2} + 5)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{df} (16 f^{2} x^{2}) + \frac{d}{df} (5)

\frac{d}{df} (16 f^{2} x^{2}) = 32 x^{2} f

\frac{d}{df} (5) = 0

= 32 x^{2} f + 0

Simplify

= 32 f x^{2}

\frac{d}{d x} (lo g_{12} (x))

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

\frac{\partial}{\partial x} (4 y^{3} sin (2 x))

\int \frac{1}{( 3 x - 1 ) ^{3}} d x

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

What is the derivative of (f(4x))^2+5 ?
The derivative of (f(4x))^2+5 is 32fx^2
What is the first derivative of (f(4x))^2+5 ?
The first derivative of (f(4x))^2+5 is 32fx^2