Calculus

Differentiation Rules

Rules of Differentiation warmup

         

If f(x)=3x2,f(x) = 3x^{2}, what is the value of f′(5)?f'(5)?

Show explanation
by Brilliant Staff

If f(x)=x12,f(x) = x^{\frac{1}{2}}, what is the value of f′(64)?f'(64)?

Show explanation
by Brilliant Staff

Suppose f(x)=x2⋅g(x),f(x) = x^2\cdot g(x), where g(5)=10g(5) = 10 and g′(5)=4.g'(5) =4.

What is the value of f′(5)?f'(5)?

Show explanation
by Brilliant Staff

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

If f(x)=(2x)(x5),f(x) = (2x)(x^5), find f′(x).f'(x).

Marla's Solution:

Apply the Product Rule: f′(x)=2(x5)+2x(5x4).f'(x) = 2(x^5) + 2x(5x^4).

Paula's Solution:

(2x)(x5)=2x6, apply the Power Rule: f′(x)=12x5.(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.

Show explanation
by Brilliant Staff

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

Show explanation
by Brilliant Staff
×

Problem Loading...

Note Loading...

Set Loading...