Compute the derivative of the given function. sin ¹(³+4) O O O d dx d dx d dx [sin ¹(x³ + 4)] = [sin ¹(₁³+ 4)] = -[sin¯¹(x³ + 4)] = d dx Isin -[sin¯¹(x^³ + 4)] = 1 √1-(x-² 1- (x^² + 4)² (x² + 4) 1 (43 √1+ (x³+4)2 (312) 3x-² 1- (x³ + 4)² 1 √ 1 − (x²³ + 4)2 (3x-²) =

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Compute the derivative of the given function.
sin ¹(x³ + 4)
O
O
O
d
-[sin ¹(x³ + 4)] =
dx
d
dx
d
dx
d
dx
√ +
1-(-³ 4) 2 (x³ + 4)
[sin ¹(x³ + 4)] =
√/1 + (x² + 4)² (3x+²)
+4)2
[sin¯¹(x³ + 4)] =
=
-[sin¯¹(x^³ + 4)] =
3x²
1 - (x³ + 4)²
1
1 – (x-³.
(3x-²)
+4)²
Transcribed Image Text:Compute the derivative of the given function. sin ¹(x³ + 4) O O O d -[sin ¹(x³ + 4)] = dx d dx d dx d dx √ + 1-(-³ 4) 2 (x³ + 4) [sin ¹(x³ + 4)] = √/1 + (x² + 4)² (3x+²) +4)2 [sin¯¹(x³ + 4)] = = -[sin¯¹(x^³ + 4)] = 3x² 1 - (x³ + 4)² 1 1 – (x-³. (3x-²) +4)²
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