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Popular >

derivative of {f}(x(2x))

Solution

\frac{d}{d x} (f (x) (2 x))

Solution

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

Solution steps

\frac{d}{d x} (f (x) (2 x))

Take the constant out:

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

= 2 \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

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

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

= 2 (\frac{d}{d x} (f (x)) x + 1 \cdot f (x))

Simplify

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

Popular Examples

integral from-1 to 1 of e^x-x^2+6

\int_{- 1}^{1} e^{x} - x^{2} + 6 d x

limit as x approaches 5 of (2-25)/(x-5)

x \to 5 lim (\frac{2 - 25}{x - 5})

sum from n=1 to infinity of 1/(e^{n+1)}

n = 1 \sum \infty \frac{1}{e ^{n + 1}}

slope of (3,-4),(5,1)slope

(3, - 4), (5, 1)

integral of (x+2)/(x^2-1)

\int \frac{x + 2}{x ^{2} - 1} d x

Frequently Asked Questions (FAQ)

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