What is the derivative of acos(bx) ?

The derivative of acos(bx) is -absin(bx)

What is the first derivative of acos(bx) ?

The first derivative of acos(bx) is -absin(bx)

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\frac{d}{d x} (a cos (b x))

- ab sin (b x)

Solution steps

\frac{d}{d x} (a cos (b x))

Take the constant out:

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

= a \frac{d}{d x} (cos (b x))

Apply the chain rule:

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

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

\frac{d}{d x} (b x) = b

= a (- sin (b x) b)

Simplify

= - ab sin (b x)

\int 4 x - \frac{4}{x} d x

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

t \frac{d y}{d t} + 5 y = t

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

\frac{d}{d x} (\frac{I n x + 1}{I n x - 1})

What is the derivative of acos(bx) ?
The derivative of acos(bx) is -absin(bx)
What is the first derivative of acos(bx) ?
The first derivative of acos(bx) is -absin(bx)