Find the derivative of f\left(x\right)=\ln\sqrt{\frac{x^3}{x+7}}

\frac{3}{2x}-\frac{1}{2\left(x+7\right)}

Find the derivative of f\left(x\right)=\sin\left(\cos\left(\tan\left(x\right)\right)\right)

the other 3 choices multiplied together

Choose the false statement about derivatives

Memorizing rules to find derivatives is the same as understanding them

Choose the false statement about derivatives

Instantaneous velocity is the derivative of average velocity

Find the derivative of f\left(x\right)=\sin\left(x^3\right)+\cos\left(x^4\right)

2\cos\left(2x\right)+3\sec^2\left(3x\right)+5e^{5x}

Find the derivative of f\left(x\right)=\sin\left(2x\right)+\tan\left(3x\right)+e^{5x}

2\cos\left(2x\right)+2\sec^2\left(3x\right)+2e^{5x}

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APC5

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Questions 10

Answers

1
The best way to represent a function is
a graph
a table
depends
an algebraic formula
2
The volume of a sphere of radius r is
\frac{4}{0}\pi^3-∞^2
\frac{4}{3}\pi r^2
\pi r^3
\frac{4}{3}\pi r^3
3
Find the derivative of f\left(x\right)=\ln\sqrt{\frac{x^3}{x+7}}
\frac{3}{2x}-\frac{1}{2\left(x+7\right)}
\frac{3}{x}-\frac{2}{\left(x+7\right)}
\sqrt{\frac{x+7}{x^3}}\left(\frac{x^3-3x^2\left(x+7\right)}{x^6}\right)
\sqrt{\frac{x+7}{x^3}}
4
Find the derivative of f\left(x\right)=\sin\left(\cos\left(\tan\left(x\right)\right)\right)
2\cos\left(2x\right)+2\sec^2\left(3x\right)+2e^{5x}
2\cos\left(2x\right)+3\sec^2\left(3x\right)+5e^{5x}
the other 3 choices multiplied together
\cos\left(2x\right)+\sec^2\left(3x\right)+e^{5x}
5
Choose the false statement about derivatives
Memorizing rules to find derivatives is the same as understanding them
Differentiation is an operation on a function that produces a derivative
Learning rules for finding derivatives is super important for calculus
The derivative is a function that describes a rate of change of a function
6
Choose the false statement about derivatives
velocity is the derivative of position
Acceleration is the derivative of velocity
Acceleration is the second derivative of position
Instantaneous velocity is the derivative of average velocity
7
Find the derivative of f\left(x\right)=\sin\left(x^3\right)+\cos\left(x^4\right)
2\cos\left(2x\right)+2\sec^2\left(3x\right)+2e^{5x}
-\frac{1}{2}\cos\left(2x\right)+\frac{1}{5}e^{5x}+C
\cos\left(2x\right)+\sec^2\left(3x\right)+e^{5x}
2\cos\left(2x\right)+3\sec^2\left(3x\right)+5e^{5x}
8
Find the equation of the tangent line to the unit circle at \left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)
y=x\sqrt{3}-\frac{1}{2}
y=x\frac{\sqrt{3}}{2}-\frac{1}{2}
y=x\sqrt{3}-2
y=x\sqrt{3}-1
9
Find the derivative of f\left(x\right)=\sin\left(2x\right)+\tan\left(3x\right)+e^{5x}
\cos\left(2x\right)+\sec^2\left(3x\right)+e^{5x}
2\cos\left(2x\right)+2\sec^2\left(3x\right)+2e^{5x}
-\frac{1}{2}\cos\left(2x\right)+\frac{1}{5}e^{5x}+C
2\cos\left(2x\right)+3\sec^2\left(3x\right)+5e^{5x}
10
Find the equation of the tangent line to the graph of f\left(x\right)=\left(x+1\right)^3at x=0
y=3\left(x+1\right)^2+1
y=3x+1
y=3x-2
y=3\left(x+1\right)^2-2

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