Question

differentiate the following w.r.t x (1+sin^2x)^2 + (1+cos^2x)^3
​

Answer 1

Step-by-step explanation:

let us suppose,

$f(x) = {(1 + { \sin}^{2}(x) )}^{2} + {(1 + { \cos}^{2} (x) )}^{3} \\ \\ f'(x) = \frac{d(f(x))}{dx} =(2) (1 + { \sin }^{2} (x))(2)( \cos(x) ) + 3({1 + { \cos}^{2} (x) )}^{2} (2)( - \sin(x) ) \\ \\ simplyfying \: \: this.... \\ \\ f'(x) = 4 \cos(x) + 4 { \sin}^{2} (x) \cos(x) - 6 \sin(x) {(1 + { \cos }^{2}(x) )}^{2} \\ \\ f'(x) = 4 { \sin }^{3} (x) \cos(x) - \sin(2x) - 12 { \cos}^{3} (x) \sin(x) - 6 { \cos }^{5} (x) \sin(x)$