What is the derivative of {f}(x(3x)) ?

The derivative of {f}(x(3x)) is 3(x derivative of {f}(x)+{f}(x))

What is the first derivative of {f}(x(3x)) ?

The first derivative of {f}(x(3x)) is 3(x derivative of {f}(x)+{f}(x))

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\frac{d}{d x} (f (x) (3 x))

3 (x \frac{d}{d x} (f (x)) + f (x))

Solution steps

\frac{d}{d x} (f (x) (3 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (f (x) x)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = f (x), g = x

= 3 (\frac{d}{d x} (f (x)) x + \frac{d x}{d x} f (x))

\frac{d x}{d x} = 1

= 3 (\frac{d}{d x} (f (x)) x + 1 \cdot f (x))

Simplify

= 3 (x \frac{d}{d x} (f (x)) + f (x))

\int sin (7 t) d t

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

\int \frac{3 ^{l n (x)}}{x} d x

\frac{\partial}{\partial u} (v^{2})

What is the derivative of {f}(x(3x)) ?
The derivative of {f}(x(3x)) is 3(x derivative of {f}(x)+{f}(x))
What is the first derivative of {f}(x(3x)) ?
The first derivative of {f}(x(3x)) is 3(x derivative of {f}(x)+{f}(x))