Question

Find derivative by first principle cos 5x

Answer 1

To find

d(cos5x)/dx=?

Let a function defined as f(x) = cos 5x

So, f(x+h) = cos 5(x+h)

Now, By first principle,

d(f(x))/dx = Lim h->0 f(x+h)-f(x)/h

d(cos5x)/dx = Lim h->0 cos5(x+h) - cos 5x / h

= lim h->0 2sin(5x-5x-5h/2)sin(5x+5x+5h/2)/h

= - Lim h->0 2sin(5h/2)sin(5x+5h/2)/h

= - Lim h->0 2(5/2) * sin(5h/2)/5h/2 * sin (5x+5h/2)

= = -5 Lim h->0 sin(5h/2)/5h/2 * Lim h->0 sin(5x+5h/2)

= -5 sin 5x

Therefore, by first principle.

d(cos 5x)/dx = -5 sin 5x

Hope this helps you !

Answer 2

Answer:

$-5sinx is right answer .................</h2><h2></h2><h2>$