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WorksheetsMathematics Grade 12 Worksheet on Unit Two
Total questions: 30
Worksheet time: 15mins
Differentiate y = (3x^2 + 2)^5
15x(3x^2 + 2)^5
60x^2(3x^2 + 2)^3
30x(3x^2 + 2)^4
6(3x^2 + 2)^5
Find the derivative of y = sin(2x^3)
3x^2 sin(2x^3)
12x^5 cos(2x^3)
6x^2 cos(2x^3)
2x^3 cos(2x^3)
Calculate dy/dx for y = e^(5x^2 + 3x)
dy/dx = e^(5x^2 + 3x) * (5x + 3)
dy/dx = e^(5x^2 + 3x) * (15x^2 + 3)
dy/dx = e^(5x^2 + 3x) * (10x + 3)
dy/dx = e^(5x^2 + 3x) * (10x + 1)
Differentiate y = ln(4x^2 + 1)
4x^2 + 1
8x / (4x^2 + 1)
2x / (4x^2 + 1)
8 / (4x^2 + 1)
Find the derivative of y = (x^2 + 1)(3x - 4)
3x^2 - 8x + 1
12x - 4
6x^2 - 4
9x^2 - 8x + 3
Calculate dy/dx for y = cos(5x^2 + 2x)
dy/dx = -5sin(5x^2 + 2x) * (10x + 2)
dy/dx = -cos(5x^2 + 2x) * (10x + 2)
dy/dx = sin(5x^2 + 2x) * (10x + 2)
dy/dx = -sin(5x^2 + 2x) * (10x + 2)
Differentiate y = (2x + 3)^4
4(2x + 3)^3
16(2x + 3)^2
8(2x + 3)^3
8(2x + 3)^4
Find the derivative of y = tan(3x^2)
3x^2 sec^2(3x)
6 sec(3x^2)
9x^2 tan(3x^2)
6x sec^2(3x^2)
Calculate dy/dx for y = (x^3 + 1)/(x - 1)
(x^3 + 3)/(x - 1)
(x^2 - 1)/(x^3 + 1)
(3x^2 + 1)/(x + 1)
(2x^3 - 3x^2 - 1) / (x - 1)^2
Differentiate y = sqrt(5x^2 + 4x)
(10x + 8) / (2sqrt(5x^2 + 4x))
(5x + 2) / (sqrt(5x^2 + 4x))
(10x^2 + 4) / (2sqrt(5x^2 + 4x))
(10x + 4) / (2sqrt(5x^2 + 4x))
Find the derivative of y = (x^2 + 2x)(x^3 - 1)
y' = 3x^4 + 6x^3 + 2x + 1
y' = 4x^4 + 8x^3 - 2
y' = 5x^4 + 12x^3 + 2x - 2
y' = 6x^4 + 4x^2 + 2x + 3
Calculate dy/dx for y = 7^(2x)
dy/dx = 2 * 7^(2x)
dy/dx = 7^(2x) * ln(2)
dy/dx = 7^(2x) * 2ln(7)
dy/dx = 14^(x) * ln(7)
Differentiate y = (sin(x^2))^3
dy/dx = 6x(sin(x^2))^2 * cos(x^2)
dy/dx = 3(sin(x^2))^2 * cos(x^2)
dy/dx = 2(sin(x^2))^3 * cos(x^2)
dy/dx = 12x^2(sin(x^2))^3 * cos(x^2)
Find the derivative of y = (x^2 + 1)^(1/2)
(1/2)(x^2 + 1)^(1/2)
2x / (x^2 + 1)^(1/2)
x / (x^2 + 1)^(1/2)
(x^2 + 1)^(1/2)
Calculate dy/dx for y = e^(sin(x))
dy/dx = e^(cos(x)) * sin(x)
dy/dx = e^(sin(x)) * sin(x)
dy/dx = e^(sin(x)) * cos(x)
dy/dx = e^(sin(x)) * -sin(x)
Differentiate y = (x^3 + 5x)(x^2 - 2)
y' = 6x^2(x^2 - 2) + 5(x^3 + 5x)
y' = 5x^2(x^2 - 2) + (x^3 + 5x)(3x^2)
y' = 3x^2(x^2 - 2) + (x^3 + 5x)(2x)
y' = 2x(x^3 + 5x) + 3x^2(x^2 - 2)
Calculate dy/dx for y = e^(3x^2 + 4x)
dy/dx = e^(3x^2 + 4x) * (9x + 4)
dy/dx = e^(3x^2 + 4x) * (6x + 4)
dy/dx = e^(3x^2 + 4x) * (3x^2 + 4)
dy/dx = e^(3x^2 + 4x) * (3x + 4)
Find the derivative of y = (x^4 + 3x)(x^2 - 1)
y' = (2x^3 + 3)(x^2 - 1) + (x^4 + 3x)(4x^3)
y' = (4x^3)(x^2 - 1) + (x^4 + 3x)(2x)
y' = (x^4 + 3x)(2x) + (4x^3)(x^2 - 1)
y' = (4x^3 + 3)(x^2 - 1) + (x^4 + 3x)(2x)
Calculate dy/dx for y = ln(3x^2 + 2x + 1)
dy/dx = (6x + 2)/(3x^2 + 2x + 1)
dy/dx = (3x + 2)/(3x^2 + 2x + 1)
dy/dx = (2x + 1)/(3x^2 + 2x + 1)
dy/dx = (6x + 2)/(2x + 1)
Find the derivative of y = (5x^3 - 2x)(x + 4)
y' = 15x^2(x + 4) + 5x^3 - 2x
y' = 5x^3 + 60x^2 - 2
y' = 20x^2 + 5x^3 - 2
y' = 15x^2(x + 4) + (5x^3 - 2x)
Differentiate y = tan(4x^2 + 1)
dy/dx = 2x sec^2(4x^2 + 1)
dy/dx = 8x^2 sec^2(4x^2 + 1)
dy/dx = 4 sec^2(4x^2 + 1)
dy/dx = 8x sec^2(4x^2 + 1)
Calculate dy/dx for y = tan(5x^2)
dy/dx = 10xsec^2(5x^2)
dy/dx = 5sec^2(5x^2)
dy/dx = 10sec^2(5x^2)
dy/dx = 5x^2sec(5x^2)
Differentiate y = (x^3 + 4x)(2x + 1)
y' = (3x^2 + 4)(2x + 1) + (x^3 + 4x)(2)
y' = (x^3 + 4x)(2) + (3x^2 + 4)(2x + 1)
y' = (3x^2 + 4)(2x + 1) + (x^3 + 4x)(1)
y' = (2x + 1)(3x^2 + 4) + (x^3 + 4x)(2)
Find the derivative of y = e^(2x^3 + x)
dy/dx = e^(2x^3 + x)(4x^2 + 1)
dy/dx = e^(2x^3 + x)(3x^2 + 1)
dy/dx = e^(2x^3 + x)(2x^2 + 1)
dy/dx = e^(2x^3 + x)(6x^2 + 1)
Calculate dy/dx for y = cos(3x^3)
dy/dx = -9x^2 sin(3x^3)
dy/dx = -3sin(3x^3)
dy/dx = -3x^2 sin(3x^3)
dy/dx = -6x^2 sin(3x^3)
Differentiate y = (x^2 + 4)(x^3 + 2)
y' = (2x)(x^3 + 2) + (x^2 + 4)(3x^2)
y' = (3x^2)(x^3 + 2) + (x^2 + 4)(2x)
y' = (2x)(x^3 + 2) + (3x^2)(x^2 + 4)
y' = (x^2 + 4)(3x^2) + (2x)(x^3 + 2)
Find the derivative of y = ln(5x^3 + 3x)
dy/dx = (3)/(5x^3 + 3x)
dy/dx = (5x^2 + 3)/(5x^3 + 3x)
dy/dx = (15x^2)/(5x^3 + 3x)
dy/dx = (15x^2 + 3)/(5x^3 + 3x)
Differentiate y = e^(x^2 + 2x)
dy/dx = e^(x^2 + 2x)(2x + 2)
dy/dx = e^(x^2 + 2x)(x + 2)
dy/dx = e^(x^2 + 2x)(2x)
dy/dx = e^(x^2 + 2x)(x^2 + 2)
Calculate dy/dx for y = sin(4x^2 + 3)
dy/dx = 8x cos(4x^2 + 3)
dy/dx = 4 cos(4x^2 + 3)
dy/dx = 8x sin(4x^2 + 3)
dy/dx = 4x cos(4x^2 + 3)
Find the derivative of y = (x^3 + 2)(x^2 + 1)
y' = (3x^2)(x^2 + 1) + (x^3 + 2)(x)
y' = (x^3 + 2)(2x) + (3x^2)(x^2 + 1)
y' = (2x)(x^3 + 2) + (3x^2)(x^2 + 1)
y' = (3x^2)(x^2 + 1) + (x^3 + 2)(2x)
