Notebook Check: Derivatives - Exponential Functions

If f(x) = ln(x), what is f'(x)

• 1/x
• x
• 1/x^2
• e^x

If f(x)=ln f(x), what is f'(x)

• 1/(f(x))^2
• f'(x)/f(x)

• f(x)^2
• 1/(ln(f(x)))^2

Find the gradient function for y equal to: y=ln(1-3x)

• -3 / (1+3x)
• -2 / (1-3x)
• -3 / (1-3x)
• -3 / (1-2x)

Find the gradient function for y equal to: y=x³ ln(x)

(Use the product rule)

• 3x^2 ln(x) + x^3
• 3x^2 ln(x) - x^2
• 2x^3 ln(x)
• 3x^2 ln(x) + x^2

Differentiate with respect to x: y=ln(xe^-x)

• (1-x)e^-x/x
• (1+x)e^-x/x
• (1-x)e^x/x
• xe^-x

Differentiate with respect to x: y=ln[x²/(x+2)(x+3)]

(Use the quotient rule)

• (2x^2 + 4x - 6) / (x^2(x + 2)(x + 4))
• (2x^2 + 4x - 6) / (x^2(x + 3)(x + 4))
• (2x^2 + 4x - 6) / (x^2(x + 2)(x + 3))
• (2x^2 + 4x - 6) / (x^2(x + 4)(x + 5))

If f(x)=e^x, what is f'(x)

• e^2
• e^x
• e^3
• e^4

If f(x) = e^f(x), what is f'(x)

• e^(f(x)) * f'(x)
• e^(f(x)) - f'(x)
• e^(f(x)) + f'(x)
• f(x) * f'(x)

Find the gradient function for y equal to: 2e^x+e^-3x

• 2e^x - 3e^(-3x)
• 2e^x + 3e^(-3x)
• 2e^x - 3e^3x
• 2e^x + e^(-3x)

Find the gradient function for y equal to: x²e^-x

(Use the product rule)

• 2xe^-x - x^2e^-x
• 2x^2e^-x - x^2e^-x
• 2xe^-x - x^2e^-x + 1
• 2xe^-x + x^2e^-x