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Popular >

derivative of-3sin(x/3)

Solution

\frac{d}{d x} (- 3 sin (\frac{x}{3}))

Solution

- cos (\frac{x}{3})

Solution steps

\frac{d}{d x} (- 3 sin (\frac{x}{3}))

Take the constant out:

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

= - 3 \frac{d}{d x} (sin (\frac{x}{3}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{3}) = \frac{1}{3}

= - 3 cos (\frac{x}{3}) \frac{1}{3}

Simplify

- 3 cos (\frac{x}{3}) \frac{1}{3} : - cos (\frac{x}{3})

= - cos (\frac{x}{3})

Popular Examples

integral of e^{3x+9}

\int e^{3 x + 9} d x

laplacetransform 7sin(4t+8)+3cos(4t-2)laplace transform

7 sin (4 t + 8) + 3 cos (4 t - 2)

limit as x approaches 1 of 1-x-[x]

x \to 1 lim (1 - x - [x])

integral of (1+x^2)

\int (1 + x^{2}) d x

derivative of (2x-3/(x^2-1))

\frac{d}{d x} (\frac{2 x - 3}{x ^{2} - 1})

Frequently Asked Questions (FAQ)

What is the derivative of-3sin(x/3) ?
The derivative of-3sin(x/3) is -cos(x/3)
What is the first derivative of-3sin(x/3) ?
The first derivative of-3sin(x/3) is -cos(x/3)