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

The derivative of (f(x(4x))^2+2) is 16(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)

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

The first derivative of (f(x(4x))^2+2) is 16(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)

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

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= 16 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2}) + 0

Simplify

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

\frac{d}{d x} (cos (a t))

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

- 0.025 x^{2} + 8 x

y^{^{'}} = x y^{2} + 2 y^{2}, y (0) = 1

f (x) = \frac{2 x ^{2} - 6 x + 5}{2 ( 2 x - 3 )}

What is the derivative of (f(x(4x))^2+2) ?
The derivative of (f(x(4x))^2+2) is 16(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)
What is the first derivative of (f(x(4x))^2+2) ?
The first derivative of (f(x(4x))^2+2) is 16(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)