Question: "Find the derivatives. y=x5(2x2−3)" - Plainmath

generals336

Answered question

2021-09-18

Find the derivatives.

y = \frac{x^{5}}{(2 x^{2} - 3)}

Answer & Explanation

berggansS

Skilled2021-09-19Added 91 answers

Step 1
given

y = \frac{x^{5}}{(2 x^{2} - 3)}

we need to find the derivative of the given equation
Step 2
For the given equation we need to find the derivative by quotient rule
The quotient rule:

\frac{d (\frac{u}{v})}{d x} = \frac{v (d \frac{u}{d x}) - u (d \frac{v}{d x})}{v^{2}}

from the given equation

v = 2 x^{2} - 3 and u = x^{5}

and u/v=y
now apply the values v,u and y values in quotient rule

\frac{d y}{d x} = \frac{(2 x^{2} - 3) 5 x^{4} - x^{5} (4 x)}{{(2 x^{2} - 3)}^{2}}

\frac{d y}{d x} = \frac{10 x^{6} - 15 x^{4} - 4 x^{6}}{4 x^{4} - 9}

\frac{d y}{d x} = \frac{6 x^{6} - 15 x^{4}}{4 x^{4} - 9}

\frac{d y}{d x} = \frac{6 x^{6} - 15 x^{4}}{4 x^{4} - 9}

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Calculus

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?
How do I find the y-intercept of a parabola?
What are the vertices of $9 x^{2} + 16 y^{2} = 144$ ?
How to determine the rate of change of a function?
Why are the tangents for 90 and 270 degrees undefined?
How to find the center and radius of the circle $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
What is multiplicative inverse of a number?
How to find the continuity of a function on a closed interval?
How do I find the tangent line of a function?
How to find vertical asymptotes using limits?
How to find the center and radius of the circle $x^{2} - 12 x + y^{2} + 4 y + 15 = 0$ ?
Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III
How to find the center and radius of the circle given $x^{2} + y^{2} + 8 x - 6 y = 0$ ?
How to find the center and radius of the circle $x^{2} + y^{2} + 4 x - 8 y + 4 = 0$ ?
How to identify the center and radius of the circle ${(x + 3)}^{2} + {(y - 8)}^{2} = 16$ ?

Didn't find what you were looking for?