Differentiation of Functions

Hey there! Can you help Priya find the derivative of f(x) = 3x^2 + 4x - 7?

• f'(x) = 6x - 4

• f'(x) = 3x^2 + 4x - 7

• f'(x) = 6x + 4

• f'(x) = 3x^2 + 4

Answer explanation

To find the derivative of f(x), apply the power rule: f'(x) = 2 * 3x^(2-1) + 1 * 4x^(1-1) + 0 = 6x + 4. Therefore, f'(x) = 6x + 4 is the correct choice.

Hey there! Let's have some fun with derivatives! What is the derivative of h(x) = e^x + ln(x)?

• What is the magical derivative of h(x) = e^x + ln(x)?

• Is it h'(x) = e^x - 1/x?

• Could it be h'(x) = e^x + x?

• Or maybe h'(x) = e^x + 1?

Answer explanation

The derivative of e^x is e^x, and the derivative of ln(x) is 1/x. Therefore, the derivative of h(x) = e^x + ln(x) is h'(x) = e^x + 1/x.

Hey there! Can you help Elijah find the derivative of k(x) = 2x^3 - 5x^2 + 8x?

• 6x^3 - 10x^2 + 8

• 6x^2 - 5x + 8

• 6x^2 - 10x + 8

• 2x^2 - 5x + 8

Answer explanation

To find the derivative of k(x), apply the power rule: 3*2x^(3-1) - 2*5x^(2-1) + 8. This simplifies to 6x^2 - 10x + 8.

Hey there! Let's have some fun with math! Lily, Emma, and Liam are competing to find the derivative of m(x) = sqrt(x) + 1/x. Can you help them out?

• x^(-1/2) - 1/x^2

• (1/2)*x^(-1/2) - 1/x

• (1/2)*x^(-1/2) - 1/x^2

• (1/2)*x^(-1/2) + 1/x^2

Answer explanation

To find the derivative of m(x) = sqrt(x) + 1/x, apply the power rule and the chain rule. The derivative is (1/2)*x^(-1/2) - 1/x^2.

Hey there! Can you assist Maya in uncovering the derivative of p(x) = 4/x + 3x^2?

• -4/x^2 + 6x

• -4/x^2 + 3x

• 4/x^2 + 6x

• -4/x + 6x^2

Answer explanation

To find the derivative of p(x) = 4/x + 3x^2, differentiate each term separately. The derivative of 4/x is -4/x^2 and the derivative of 3x^2 is 6x. Therefore, the derivative of p(x) is -4/x^2 + 6x.

Hey there! Abigail, Rohan, and Luna are having a blast in their math class! Can you help them find the derivative of the function r(x) = e^(2x) + 1/x^2?

• e^(2x) - 1/x^3

• 4e^(2x) - 2/x^3

• 2e^(2x) - 2/x^3

• 2e^(2x) + 2/x^3

Answer explanation

The derivative of e^(2x) is 2e^(2x), and the derivative of 1/x^2 is -2/x^3. Therefore, the derivative of r(x) = e^(2x) + 1/x^2 is 2e^(2x) - 2/x^3.

Hey there! Can you help Mia find the derivative of s(x) = 5x^4 - 2x^3 + 7x^2?

• s'(x) = 20x^3 - 6x^2 + 7x

• s'(x) = 20x^3 - 6x^2 + 14x

• s'(x) = 15x^4 - 2x^3 + 7x^2

• s'(x) = 5x^3 - 2x^2 + 7

Answer explanation

To find the derivative of s(x), apply the power rule to each term: s'(x) = 20x^3 - 6x^2 + 14x. Therefore, the correct choice is s'(x) = 20x^3 - 6x^2 + 14x.

Hey there! Let's make math more exciting! What's the derivative of u(x) = tan(x) - cot(x)?

• sec(x) - csc(x)

• sec^2(x) - csc^2(x)

• sec^2(x) + csc^2(x)

• sec(x) + csc(x)

Answer explanation

The derivative of tan(x) is sec^2(x) and the derivative of cot(x) is -csc^2(x). Therefore, the derivative of u(x) = tan(x) - cot(x) is sec^2(x) - (-csc^2(x)) = sec^2(x) + csc^2(x).

Hey there! Can you help Charlotte find the derivative of v(x) = 3/x + 2x^3?

• -3/x^2 + 2x^2

• -3/x^2 + 6x^2

• 3/x^2 + 6x^2

• -3/x^2 + 2x^3

Answer explanation

The derivative of v(x) = 3/x + 2x^3 is -3/x^2 + 6x^2. The derivative of 3/x is -3/x^2 and the derivative of 2x^3 is 6x^2.

Hey there! Let's have some fun with derivatives. What is the derivative of w(x) = sin(x) + cos(2x)?

• cos(x) - sin(2x)

• sin(x) - 2cos(2x)

• cos(x) - 2sin(2x)

• cos(x) + 2sin(2x)

Answer explanation

The derivative of sin(x) is cos(x) and the derivative of cos(2x) is -2sin(2x), so the derivative of w(x) = sin(x) + cos(2x) is cos(x) - 2sin(2x).