Question 1. If \(y=\tan(\sin(x^2))\), then \(y'=\cos(x^2)\sec^2(\sin(x^2))\).
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: False
Question 2. \( \frac{d^{100}}{dx^{100}}(\sin x)=?\)
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: \(\sin x\)
Question 3. If \(f(x)=\cos(3x)\), then \(f'(x)=\)?
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: \(-3\sin(3x)\)
Question 4. If \(f(x)=\cos x\tan x\), then \(f'(x)=\)?
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: \(\cos x\)
Question 5. Statement is true?
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: False
Question 6. If \(y=\log_7(x^2)\), then \(y'=\frac{2}{x\ln7}\).
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: True
Question 7. If \(y=e^x\ln x\), then \(y'=e^x(\frac1x+\ln x)\).
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: True
Question 8. Derivative of \(y=(3x)^{x+5}\) is \(3(x+5)(3x)^{x+4}\).
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: False
Question 9. Find \(dy/dx\) if \(y^4=4x\).
Step 1: Apply the appropriate differentiation rule. Step 2: Simplify the expression. Answer: \(\frac1{y^3}\)
