The derivative of with respect to is
Answer and explanation
Correct answer: B.
Step 2. Use the trigonometric identity .
Step 3. Evaluate the limit: $displaystylelim_{h o 0}cosleft(x + dfrac{h}{2} ight) imes lim_{h o 0}dfrac{sin(h/2)}{h/2} = (cos x)(1) = cos x$.
Step 3. Evaluate the limit: $displaystylelim_{h o 0}cosleft(x + dfrac{h}{2} ight) imes lim_{h o 0}dfrac{sin(h/2)}{h/2} = (cos x)(1) = cos x$.
- Step 1: State the first-principles derivative definition for : .
Answer
.
Why not the others: introduces a negative sign error, is the original function without differentiation, and is the second derivative.
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