What is the derivative of cos(a3+x3)?

3 Answers
Jun 20, 2016

(3x2)(sin(a3+x3))

Explanation:

Use chain rule for derivatives.

Consider this as ddx(cos(f(x))) where f(x) = a3+x3

The answer would be composition of derivatives of cos(x) (and putting x as f(x) after differentiating and f(x). Let me demonstrate this in this question.

Derivative of cos(x) is sin(x). Now, let's substitute x with f(x)

So the answer is (sin(f(x))×(ddx(f(x)))).

Now, f(x)=a3+x3. Assuming a to be a constant, a3 is a constant and derivative of a constant is 0. Derivative of x3 is 3x2. I won't explain this because you need to learn this yourself if you can't already figure it out.

So back to the answer.

Ans: (sin(a3+x3)×(ddx(a3+x3)))

Final Ans: 3x2×sin(a3+x3)

Jun 20, 2016

Just another way of saying the same thing

dydx=3x2sin(a3+x3)

Explanation:

Let u=a3+x3 dudx=3x2

Let y=cos(u) dydu=sin(u)

But dydx=dudx×dydu

dydx=3x2sin(a3+x3)

Jun 20, 2016

ddx=sin(a3+x3)3x2

Explanation:

the main function is cos(x)
the sub function is a3+x3
by the chain rule
main function should differentiate first ,and then differentiate sub function
so
ddx=sin(a3+x3)3x2