Question

Find the derivative
Best answer be marked brainliest!!
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Answer 1

Given: Given expression is

${x}^{ - 3} (5 + 3x)$

To find: We have to find its derivative.

Solution:

To find the derivative of the above expression we have to follow the below steps-

As there two functions of x is present so, we have to apply u.dv+v.du rule.

Applying the above rule the derivative of the expression is as follows-

$\frac{d}{dx} ( {x}^{ - 3} .(5 + 3x)) \\ {x}^{ - 3} \frac{d}{dx}(5 + 3x) + (5 + 3x)\frac{d}{dx}( {x}^{ - 3} ) \\ {x}^{ - 3} (0 + 3) + (5 + 3x)( - 3 {x}^{ - 4} ) \\ = 3 {x}^{ - 3} - 15 {x}^{ - 4} - 9 {x}^{ - 3} \\ = - 3 {x}^{ - 3} (5 {x}^{ - 1} + 2)$

The derivative of the expression is $- 3 {x}^{ - 3} (5 {x}^{ - 1} + 2)$.