Differentiate y = √x^3 (for x > 0 ) with respect to x.

Worked solution for TMUA-P1-MM6-004 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM6-004 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM6-004 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM6-004?

No — calculators are banned in the TMUA. TMUA-P1-MM6-004 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM6-004?

TMUA-P1-MM6-004 is Paper P1 · Differentiation (specification code MM6), level 2. Drill more of the same topic from this page.

TMUA-P1-MM6-004 — Paper P1 · Differentiation · Level 2

P1MM6Level 2~180s target

Spec: MM6 · No calculator · ~180s

Differentiate

y = \sqrt{x^3}

(for

x > 0

) with respect to

x

Options

$\dfrac{3}{2}\sqrt{x}$
$\dfrac{2}{3}\sqrt{x}$
$\dfrac{3}{2\sqrt{x}}$
$x^{1/2}$
$\dfrac{1}{2\sqrt{x}}$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: fractional-powers, surd-rewrite. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Write

\sqrt{x^3} = x^{3/2}

, then

\frac{d}{dx} = \frac{3}{2}x^{1/2} = \frac{3}{2}\sqrt{x}

. Trap:

\frac{3}{2\sqrt{x}}

differentiates as if the power were

\frac{1}{2}

— plausible if you read

\sqrt{x^3}

\sqrt{x}

cubed the wrong way round.

Keep practising

Same topic · same level
P1MM6Level 2
TMUA-P1-MM6-005
Let f(x) = x^2 + 4x/x for x ≠ 0. What is f'(x)?
Differentiation
Open TMUA-P1-MM6-005 →
Step up a level
P1MM6Level 3
TMUA-P1-MM6-009
The area of a circle is A = π r^2. The radius increases at 2 cm/s. At what rate is the area increasing when r = 5 cm?
Differentiation
Open TMUA-P1-MM6-009 →
More in this topic
P1MM6Level 2
TMUA-P1-MM6-006
Find the equation of the tangent to y = x^2 at the point where x = 2.
Differentiation
Open TMUA-P1-MM6-006 →

Browse more

Loading…

Keep practising

Same topic · same level

P1MM6Level 2

TMUA-P1-MM6-005

Let f(x) = x^2 + 4x/x for x ≠ 0. What is f'(x)?

Differentiation

Open TMUA-P1-MM6-005 →

Step up a level

P1MM6Level 3

TMUA-P1-MM6-009

The area of a circle is A = π r^2. The radius increases at 2 cm/s. At what rate is the area increasing when r = 5 cm?

Differentiation

Open TMUA-P1-MM6-009 →

TMUA-P1-MM6-004 — Paper P1 · Differentiation · Level 2

Options

Keep practising

Master Differentiation

TMUA-P1-MM6-004 — Paper P1 · Differentiation · Level 2

Options

Keep practising

Master Differentiation