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

The derivative of (f(x(4x))^2+5) is 16(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)

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

The first derivative of (f(x(4x))^2+5) 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} + 5)

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} + 5)

Simplify

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

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

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} (5)

\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} (5) = 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})

6 x + y^{2} = 16, x = y

\frac{d}{d x} (3 a x^{4} - 4 a x^{3} - 5 b x^{2} + 7 c x)

\int (\frac{1}{x ^{- 3}} + x^{2} e^{3 x^{3}} - \frac{8}{x}) d x

y^{^{'}} + 6 y = e^{- t} - 6

\int e^{4 x} - 5 sin (x) d x

What is the derivative of (f(x(4x))^2+5) ?
The derivative of (f(x(4x))^2+5) is 16(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)
What is the first derivative of (f(x(4x))^2+5) ?
The first derivative of (f(x(4x))^2+5) is 16(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)