What is the derivative of (80sin(0.6x)/x+15) ?

The derivative of (80sin(0.6x)/x+15) is (80(0.6xcos(0.6x)-sin(0.6x)))/(x^2)

What is the first derivative of (80sin(0.6x)/x+15) ?

The first derivative of (80sin(0.6x)/x+15) is (80(0.6xcos(0.6x)-sin(0.6x)))/(x^2)

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\frac{d}{d x} (\frac{80 sin ( 0.6 x )}{x} + 15)

\frac{80 ( 0.6 x cos ( 0.6 x ) - sin ( 0.6 x ) )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{80 sin ( 0.6 x )}{x} + 15)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{80 sin ( 0.6 x )}{x}) + \frac{d}{d x} (15)

\frac{d}{d x} (\frac{80 sin ( 0.6 x )}{x}) = \frac{80 ( 0.6 x cos ( 0.6 x ) - sin ( 0.6 x ) )}{x ^{2}}

\frac{d}{d x} (15) = 0

= \frac{80 ( 0.6 x cos ( 0.6 x ) - sin ( 0.6 x ) )}{x ^{2}} + 0

Simplify

= \frac{80 ( 0.6 x cos ( 0.6 x ) - sin ( 0.6 x ) )}{x ^{2}}

What is the derivative of (80sin(0.6x)/x+15) ?
The derivative of (80sin(0.6x)/x+15) is (80(0.6xcos(0.6x)-sin(0.6x)))/(x^2)
What is the first derivative of (80sin(0.6x)/x+15) ?
The first derivative of (80sin(0.6x)/x+15) is (80(0.6xcos(0.6x)-sin(0.6x)))/(x^2)