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

The derivative of {f}(x(-x)) is -x derivative of {f}(x)-{f}(x)

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

The first derivative of {f}(x(-x)) is -x derivative of {f}(x)-{f}(x)

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Popular >

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

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

Solution steps

\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

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

\frac{d}{d x} (- x) = - 1

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

Simplify

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

20 x^{\frac{7}{5}} - 6 x^{\frac{2}{13}}

\int 2 e^{- 2 t} d t

x^{5}

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

\frac{\partial}{\partial y} (5 y^{2} e^{5 x y})

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