What is power rule on a^x for a ≠ e?

(d)/(dx)(2^x) is not x · 2^x - 1. Use 2^x = e^x ln 2 and the chain rule: (d)/(dx)(2^x) = (ln 2) · 2^x.

Differentiate y = e^xx. [3 marks]

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VICMath MethodsQuick questions

Unit 3

Quick questions on Differentiation rules and standard derivatives: VCE Math Methods Unit 3

Q: What is worked example?

Differentiate f(x) = x^2 e^3 x.

Q: What is sign error in the quotient rule?

The numerator is u' v minus u v', in that order. Reversing it flips the sign.

Q: What is q1?

Differentiate y = (2x + 1)^5. [2 marks]

Q: What is q2?

Differentiate f(x) = x^2 sin x. [3 marks]

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is worked example?

Show answer

Differentiate

f(x) = x^2 e^{3 x}

What is sign error in the quotient rule?

Show answer

The numerator is

u' v

minus

u v'

, in that order. Reversing it flips the sign.

What is power rule on

a^x

for

a \neq e

Show answer

\frac{d}{dx}(2^x)

is not

x \cdot 2^{x - 1}

. Use

2^x = e^{x \ln 2}

and the chain rule:

\frac{d}{dx}(2^x) = (\ln 2) \cdot 2^x

What is q1?

Show answer

Differentiate

y = (2x + 1)^5

. [2 marks]

What is q2?

Show answer

Differentiate

f(x) = x^2 \sin x

. [3 marks]

What is q3?

Show answer

Differentiate

y = \dfrac{e^x}{x}

. [3 marks]

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