What is the derivative of x/(10sin(5x)) ?

The derivative of x/(10sin(5x)) is 1/10 (sin(5x)+5xcos(5x))

What is the first derivative of x/(10sin(5x)) ?

The first derivative of x/(10sin(5x)) is 1/10 (sin(5x)+5xcos(5x))

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\frac{d}{d x} (\frac{x}{10} sin (5 x))

\frac{1}{10} (sin (5 x) + 5 x cos (5 x))

Solution steps

\frac{d}{d x} (\frac{x}{10} sin (5 x))

Take the constant out:

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

= \frac{1}{10} \frac{d}{d x} (x sin (5 x))

Apply the Product Rule:

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

f = x, g = sin (5 x)

= \frac{1}{10} (\frac{d x}{d x} sin (5 x) + \frac{d}{d x} (sin (5 x)) x)

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= \frac{1}{10} (1 \cdot sin (5 x) + cos (5 x) \cdot 5 x)

Simplify

= \frac{1}{10} (sin (5 x) + 5 x cos (5 x))

\int e^{2 l n (y)} \cdot e^{y} d y

x \to - 1 lim (\frac{x ^{2} - 4}{1 - x})

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

\frac{d y}{d x} = 2 x y^{- 2}

f (x) = a^{8} + cos^{8} (x)

What is the derivative of x/(10sin(5x)) ?
The derivative of x/(10sin(5x)) is 1/10 (sin(5x)+5xcos(5x))
What is the first derivative of x/(10sin(5x)) ?
The first derivative of x/(10sin(5x)) is 1/10 (sin(5x)+5xcos(5x))