If f ( x ) = 3 x 2 + x + 2 and g ( x ) = x + 4 3 , what is the derivative (f*g)'(x)?

Set up the composite result function.f(g(x))Evaluate&nbsp;f(x+43)&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(x+43)=3(x+43)2+x+43+2Remove parentheses.f(x+43)=3(x+43)2+x+43+2Rewrite&nbsp;x+432&nbsp;as&nbsp;((x+4)2)13.f(x+43)=3(x+4)32+x+43+2

"If f ( x ) = 3 x..." was answered by our community

College
Calculus and Analysis
Differential Calculus
Derivatives

lifretatox8n

Answered question

2022-05-13

f (x) = 3 x^{2} + x + 2

and

g (x) = \sqrt[3]{x + 4}

, what is the derivative (f*g)'(x)?

Answer & Explanation

verdesett014ci

Beginner2022-05-14Added 18 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (\sqrt[3]{x + 4})$ by substituting in the value of $g$ into $f$ .

$f (\sqrt[3]{x + 4}) = 3 {(\sqrt[3]{x + 4})}^{2} + \sqrt[3]{x + 4} + 2$

Remove parentheses.

$f (\sqrt[3]{x + 4}) = 3 {(\sqrt[3]{x + 4})}^{2} + \sqrt[3]{x + 4} + 2$

Rewrite ${\sqrt[3]{x + 4}}^{2}$ as ${({(x + 4)}^{2})}^{\frac{1}{3}}$ .

$f (\sqrt[3]{x + 4}) = 3 {\sqrt[3]{(x + 4)}}^{2} + \sqrt[3]{x + 4} + 2$

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?