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Questions and Answers
What is the derivative of the function $f(x) = x^3 - 3x^2 + 4$ evaluated at $x = 2$?
What is the derivative of the function $f(x) = x^3 - 3x^2 + 4$ evaluated at $x = 2$?
- 4
- 6 (correct)
- 2
- 0
What is the derivative of $y = e^{2x}$ with respect to $x$?
What is the derivative of $y = e^{2x}$ with respect to $x$?
- (1/2)e^{2x}
- e^{2x}
- 2e^x
- 2e^{2x} (correct)
What is the second derivative of the function $f(x) = an(x)$?
What is the second derivative of the function $f(x) = an(x)$?
- sec^2(x)tan(x)
- 2sec^2(x)
- sec^2(x)
- 2sec^2(x)tan(x) (correct)
What is the derivative of $ln(sin(x))$ with respect to $x$?
What is the derivative of $ln(sin(x))$ with respect to $x$?
What is the derivative of the function $f(x) = ext{arctan}(x)$ with respect to $x$?
What is the derivative of the function $f(x) = ext{arctan}(x)$ with respect to $x$?
If f(x) = x^3 - 3x^2 + 4, then what is f'(2)?
If f(x) = x^3 - 3x^2 + 4, then what is f'(2)?
What is the derivative of sin^(-1)(x) with respect to x?
What is the derivative of sin^(-1)(x) with respect to x?
If y = e^(2x), then what is dy/dx?
If y = e^(2x), then what is dy/dx?
What is the second derivative of f(x) = ln(x)?
What is the second derivative of f(x) = ln(x)?
If f(x) = tan(x), what is f'(x)?
If f(x) = tan(x), what is f'(x)?
What is the derivative of cos(x^2) with respect to x?
What is the derivative of cos(x^2) with respect to x?
If y = x * e^x, what is dy/dx?
If y = x * e^x, what is dy/dx?
What is the derivative of arctan(x) with respect to x?
What is the derivative of arctan(x) with respect to x?
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Study Notes
Differentiation Questions - TS EAMCET
- Question 1: If f(x) = x³ - 3x² + 4, then f'(2) is. Possible answers: A) 0, B) 2, C) 4, D) 6.
- Question 2: The derivative of sin⁻¹(x) with respect to x is. Possible answers: A) 1/√(1 - x²), B) -1/√(1 - x²), C) √(1 - x²), D) -√(1 - x²).
- Question 3: If y = e^(2x), then dy/dx is. Possible answers: A) e^(2x), B) 2e^(2x), C) (1/2)e^(2x), D) 2e^x.
- Question 4: The second derivative of f(x) = ln(x) is. Possible Answers: A) -1/x², B) 1/x², C) 1/x, D) -1/x.
- Question 5: If f(x) = tan(x), then f'(x) is. Possible answers: A) 2sec²(x)tan(x), B) sec²(x), C) sec²(x)tan(x), D) 2sec²(x).
- Question 6: The derivative of cos(x²) with respect to x is. Possible answers: A) -2xsin(x²), B) -xsin(x²), C) -2sin(x²), D) -sin(x²).
- Question 7: If y = x * eˣ, then dy/dx is. Possible answers: A) eˣ, B) x * eˣ, C) (x + 1) * eˣ, D) (x - 1) * eˣ.
- Question 8: The derivative of ln(sin(x)) with respect to x is. Possible answers: A) cot(x), B) csc(x), C) sec(x), D) tan(x).
- Question 9: If f(x) = √x, then f'(x) is. Possible answers: A) 1/(2√x), B) 1/√x, C) 2√x, D) √x.
- Question 10: The derivative of arctan(x) with respect to x is. Possible answers: A) 1/(1 + x²), B) -1/(1 + x²), C) 1/(1 - x²), D) -1/(1 - x²).
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