Practice question · Fill in the blanks
Complete the chain rule applied to a specific composition.
The derivative of sin(x^2) is ______.
Word bank: cos(x^2) · cos(2x) · cos(x^2) times 2x · 2x cos x
Hints
- Differentiate the outer sine, leaving its argument exactly as it stands, then multiply.
- The inner function is x^2, whose derivative is 2x.
Show the answer
The derivative of sin(x^2) is cos(x^2) times 2x.
Why
The outer derivative gives cos(x^2) and the inner derivative contributes a factor of 2x. Answering cos(x^2) alone is exactly the omission the lesson warns about, and differentiating inside the cosine to get cos(2x) misapplies the rule at the wrong level.
Practise Differentiation Rules
The app has 6 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.