"Find the derivatives of the following function. y=tan−1−9⋅x3..." was answered by our experts

Tazmin Horton

Answered question

2021-09-22

Find the derivatives of the following function.
$y = \tan^{- 1} - 9 \cdot x^{3}$
y'=

Answer & Explanation

curwyrm

Skilled2021-09-23Added 87 answers

Step 1
Given function,

y = \tan^{- 1} - 9 \cdot x^{3}

Step 2
Using the chain rule of the derivative,

\frac{d y}{d x} = \frac{d y}{d t} \frac{d t}{d x}

Let

- 9 x^{3} = t \Rightarrow y = \tan^{- 1} (t)

Now the derivative of y with respect to x,

y^{'} = \frac{d (\tan^{- 1} (t))}{d t} \frac{d (- 9 x^{3})}{d x}

y^{'} = \frac{1}{1 + t^{2}} (- 27 x^{2})

y^{'} = \frac{- 27 x^{2}}{1 + {(- 9 x^{3})}^{2}}

y^{'} = \frac{- 27 x^{2}}{1 + 81 x^{6}}

Step 3
Final answer:

y^{'} = \frac{- 27 x^{2}}{1 + 81 x^{6}}

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?