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

The derivative of (f(x(5x))^2-2) is 25(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)

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

The first derivative of (f(x(5x))^2-2) is 25(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)

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

25 (2 x^{2} f (x) \frac{d}{d x} (f (x)) + 2 x f (x)^{2})

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= 25 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2}) - 0

Simplify

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

x \to 4 lim (\frac{7 x + 6}{3 x - 2})

\frac{d}{d x} ((x^{\frac{3}{2}})^{2})

\int \frac{x ^{2} - 5 x + 16}{( 2 x + 1 ) ( x - 2 ) ^{2}} d x

\frac{\partial}{\partial y} (e^{x} y)

\frac{x d y}{d x} + y = \frac{1}{y ^{2}}

What is the derivative of (f(x(5x))^2-2) ?
The derivative of (f(x(5x))^2-2) is 25(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)
What is the first derivative of (f(x(5x))^2-2) ?
The first derivative of (f(x(5x))^2-2) is 25(2x^2{f}(x) derivative of {f}(x)+2x{f}(x)^2)