Question

find the derivatis of the following w.r.t.x
3x² - 4÷x+5​

Answer 1

Answer:

3x²– 4 = x + 5 (3x – 5) + 16 ans

Answer 2

Answer:

The derivative of the function   $f(x)=\frac{3x^{2}-4 }{x+5}$ with respect to x  ​ is $=\frac{3x^{2} +30x+4}{x^{2} +10x+25}$

Step-by-step explanation:

A derivative is the rate of change of a function with respect to an independent variable

From the question, it is given that the function is

$f(x)=\frac{3x^{2}-4 }{x+5}$

there are two functions one in the denominator and one in the numerator

so we have to use the quotient rule to find the derivative

the statement of the quotient rule is

if U and V are two differentiable functions then the derivative of U/V is equal to

$\left(\frac{u}{v}\right)^1=\frac{vu^1-uv^1}{v^2}$

here $u=3 x^{2} -4$ and $v=x+5$

now $u'=6x$ and $v'=1$

substitute these values

$(u/v)'=\frac{(x+5)6x-(3x^{2} -4)}{(x+5)^{2} }$

          $=\frac{3x^{2} +30x+4}{x^{2} +10x+25}$