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Popular >

derivative of xarccos(3x)

Solution

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

Solution

arccos (3 x) - \frac{3 x}{1 - 9 x ^{2}}

Solution steps

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

Apply the Product Rule:

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

f = x, g = arccos (3 x)

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

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

\frac{d}{d x} (arccos (3 x)) = - \frac{3}{1 - 9 x ^{2}}

= 1 \cdot arccos (3 x) + (- \frac{3}{1 - 9 x ^{2}}) x

Simplify

1 \cdot arccos (3 x) + (- \frac{3}{1 - 9 x ^{2}}) x : arccos (3 x) - \frac{3 x}{1 - 9 x ^{2}}

= arccos (3 x) - \frac{3 x}{1 - 9 x ^{2}}

Popular Examples

integral from-2 to 4 of 1/((x-3)^3)

\int_{- 2}^{4} \frac{1}{( x - 3 ) ^{3}} d x

implicit (dy)/(dx),y=2x^3 implicit derivative

\frac{d y}{d x}, y = 2 x^{3}

integral of e^{3x}sin(4x)

\int e^{3 x} sin (4 x) d x

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

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

laplacetransform 1+0.1e^{-0.02t}laplace transform

1 + 0.1 e^{- 0.02 t}

Frequently Asked Questions (FAQ)

What is the derivative of xarccos(3x) ?
The derivative of xarccos(3x) is arccos(3x)-(3x)/(sqrt(1-9x^2))
What is the first derivative of xarccos(3x) ?
The first derivative of xarccos(3x) is arccos(3x)-(3x)/(sqrt(1-9x^2))