With f ( x ) = ln ⁡ ( 5 x + 5 ) and g ( x ) = tan ⁡ ( π x 2 ), find the derivative of the product (f*g)(x).

Set up the composite result function.f(g(x))Evaluate&nbsp;f(tan(πx2))&nbsp;by substituting in the value of&nbsp;g&nbsp;into&nbsp;f.f(tan(πx2))=ln(5(tan(πx2))+5)Multiply&nbsp;5&nbsp;by&nbsp;tan(πx2).f(tan(πx2))=ln(5tan(πx2)+5)

Resolved: "With f ( x ) = ln ⁡..."

College
Calculus and Analysis
Differential Calculus
Derivatives

sembuang711q6

Answered question

2022-05-12

With

f (x) = \ln (5 x + 5)

and

g (x) = \tan (\frac{π x}{2})

, find the derivative of the product (f*g)(x).

Answer & Explanation

Elliana Shelton

Beginner2022-05-13Added 14 answers

Set up the composite result function.

$f (g (x))$

Evaluate $f (\tan (\frac{π x}{2}))$ by substituting in the value of $g$ into $f$ .

$f (\tan (\frac{π x}{2})) = \ln (5 (\tan (\frac{π x}{2})) + 5)$

Multiply $5$ by $\tan (\frac{π x}{2})$ .

$f (\tan (\frac{π x}{2})) = \ln (5 \tan (\frac{π x}{2}) + 5)$

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?