Question

Find the derivative of the function. y = a7 + cos7 x.

Answer 1

yas, I'm learning this

remember
f'(a+b)=f'(a)+f'(b)
and
f'(cos(x))=-sin(x)
and
f'(g(x))=f'(g(x))g'(x)
and
f'(xⁿ)=nxⁿ⁻¹


f'(a⁷+cos(7x))=
f'(a⁷)+f'(cos(7x))=
7a⁶+f'(cos(7x))f'(7x)=
7a⁶-sin(7x)(7f'(x))=
7a⁶-sin(7x)(7*1)=
7a⁶-sin(7x)(7)=
7a⁶-7sin(7x)


f'(a⁷+cos(7x))=7a⁶-7sin(7x)

Answer 2

The derivative of the function.
y = x^7 + cos7 x.
dy/dx = 7x^6 - 7sin 7x
Enjoy!