1.3 Differentiation

What is the derivative of

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Find the second derivative of:

f(x) = 2x² - 8x + 9

• -8

• 4

• 9

• 0

Calculate the gradient of f(x)=ln(x)+x at x=2/3

• 0.261

• 2.5

• 1.5

• -0.405

When do you use the chain rule?

• anytime you want

• when there is a function in a function

• where there are multiple layers to a lasagna (yum)

• when there is division

What rule best apply to find the derivative of y=x lnx

• product rule

• quotient rule

• power rule

• sum rule

Find the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)

• 3x²
• x³
• 6x
• 3x² + x³