Differentiation Rules

Rules of Differentiation warmup

If $f(x) = 3x^{2},$ what is the value of $f'(5)?$

225 75 30 60

by Brilliant Staff

If $f(x) = x^{\frac{1}{2}},$ what is the value of $f'(64)?$

\frac{1}{16}

8

16

\frac {1}{128}

by Brilliant Staff

Suppose $f(x) = x^2\cdot g(x),$ where $g(5) = 10$ and $g'(5) =4.$

What is the value of $f'(5)?$

40 100 200 250

by Brilliant Staff

Marla and Paula are confronted with the following question on their calculus exam:

If $f(x) = (2x)(x^5),$ find $f'(x).$

Marla's Solution:

Apply the Product Rule: $f'(x) = 2(x^5) + 2x(5x^4).$

Paula's Solution:

$(2x)(x^5) = 2x^6 \mbox{, apply the Power Rule: } f'(x) = 12x^5.$

Who got it right?

Note. The grader does not require the answer to be fully simplified.

Marla only Paula only Both Marla and Paula Neither

by Brilliant Staff

If $f(x) = (10x + 1)^{50},$ what is the value of $f'(0)?$

1 500 600 0

by Brilliant Staff

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