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  1. AP Calculus
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Fundamentals of Differentiation

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

What is the derivative of 1x6\frac{1}{x^6}x61​?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

What is the derivative of the polynomial p(r)=r7+rp(r)=r^{7}+rp(r)=r7+r?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

What is the derivative of root of 5 to x^2?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

If a student is applying the power rule to differentiate the function f(x)=x5f(x) = x^5f(x)=x5, what is the derivative of this function?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

Given the function g(t)=t3/2g(t) = t^{3/2}g(t)=t3/2, what would be its instantaneous rate of change at any point t using differentiation?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

Which of the following functions can't be differentiated using the Power Rule?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

How do you calculate the derivative of the function k(z)=z10k(z)=z^{10}k(z)=z10?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

If f(x)=x5f(x) = x^5f(x)=x5, what is the derivative of f(x)f(x)f(x) with respect to xxx?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

What is the derivative of the function f(x)=x5f(x) = x^5f(x)=x5?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

If you apply the power rule to differentiate the function given by x3\sqrt[3]{x}3x​, what will be its derivative?