Find the derivative of $f ( x ) = \frac { \tan x } { x ^ { 3 } }$ .
A) $\frac { \sec x } { 3 x ^ { 2 } }$

B) $\frac { x \sec ^ { 2 } x - 3 \tan x } { x ^ { 4 } }$.

C) $\frac { \sec ^ { 2 } x } { 3 x ^ { 2 } }$
D) $\frac { x \sec ^ { 2 } x - 3 \tan x } { x ^ { 4 } }$
E) $\frac { \tan x } { 3 x ^ { 2 } }$
F) $\frac { x \sec x - 3 \tan x } { x ^ { 4 } }$
G) $\frac { \sec ^ { 2 } x } { x ^ { 3 } }$

H)None of the above

Question

Find the derivative of $f ( x ) = \frac { \tan x } { x ^ { 3 } }$ .
A) $\frac { \sec x } { 3 x ^ { 2 } }$

B) $\frac { x \sec ^ { 2 } x - 3 \tan x } { x ^ { 4 } }$.

C) $\frac { \sec ^ { 2 } x } { 3 x ^ { 2 } }$ 
D) $\frac { x \sec ^ { 2 } x - 3 \tan x } { x ^ { 4 } }$
E) $\frac { \tan x } { 3 x ^ { 2 } }$
F) $\frac { x \sec x - 3 \tan x } { x ^ { 4 } }$
G) $\frac { \sec ^ { 2 } x } { x ^ { 3 } }$
 
H)None of the above

Quizplus · Accepted Answer

Using the quotient rule, we have:$$f'(x) = \frac{(x^3)(\sec^2 x) - (	an x)(3x^2)}{(x^3)^2} = \frac{x^3\sec^2 x - 3x^2	an x}{x^6} = \frac{x\sec^2 x - 3	an x}{x^4}$$

Find the Derivative Of f(x)=tan⁡xx3f ( x ) = \frac { \tan x } { x ^ { 3 } }f(x)=x3tanx​

Find the Derivative Of $f ( x ) = \frac { \tan x } { x ^ { 3 } }$