10 questions🇬🇧English
⚡ Chain, Product & Quotient Rules – A-level
Maths · A-level — practises differentiating composite, product and quotient functions, including trig, e^x and ln x
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Questions
Differentiate y = (3x + 1)⁵ with respect to x.
15(3x + 1)⁴
5(3x + 1)⁴
3(3x + 1)⁴
15(3x + 1)⁵
20s
What is the derivative of y = e^(4x)?
4x e^(4x − 1)
e^(4x)
4e^(4x)
¼e^(4x)
20s
What is the derivative of y = ln(5x)?
1/x
ln 5 / x
5/x
1/(5x)
20s
Differentiate y = sin(x²) with respect to x.
−2x cos(x²)
cos(2x)
2x cos(x²)
cos(x²)
30s
Use the product rule to differentiate y = x²eˣ.
eˣ(x² + 2)
x²eˣ + 2x
2xeˣ
eˣ(x² + 2x)
30s
What is the derivative of y = tan(3x)?
sec²(3x)
3sec(3x)tan(3x)
−3sec²(3x)
3sec²(3x)
20s
Use the quotient rule to differentiate y = (sin x) / x.
(x cos x − sin x) / x²
cos x
(x cos x + sin x) / x²
(sin x − x cos x) / x²
30s
Find the gradient of the curve y = ln(x² + 3) at the point where x = 1.
2
ln 4
½
¼
30s
The curve y = x ln x, for x > 0, has one stationary point. What is its x-coordinate?
e²
1
1/e
e
60s
Differentiate y = x(2x + 1)³ and fully factorise the answer.
(2x + 1)²(5x + 1)
(2x + 1)²(7x + 1)
(2x + 1)²(8x + 1)
6x(2x + 1)²
60s