Question

Differentiate w.r.t. x the function
sin³x + cos⁶x

Answer 1

Answer:

y=sin³x + cos⁶x

dy/dx=2sin²x cox³x-6cos⁵xsin⁶x

Answer 2

Step-by-step explanation:

Given: sin³x + cos⁶x

let y = sin³x + cos⁶x

Now, differentiating with respect to X.

dy/dx = d(sin³x + cos⁶x)/dx

dy/dx = d(sin³x)/dx + d(cos⁶x)/dx

dy/dx = 3 sin²x d(sinx)/dx + 6 (cos^5x)/ dx

dy/dx = 3 sin²x . cos x + 6 cos^5x .(-sinx)

dy/dx = 3 sin²x . cos x - 6 sinx cos^5x

dy/dx = 3 sinx . cos x ( sinx - 2 cos⁴x)

hence dy/dx = 3 sinx . cos x ( sinx - 2 cos⁴x)

Hope this will be helpful to you.... !!!!!