BASCAL PROJECT

BASCALEARNING

Practice and gain more knowledge about basic calculus in an interactive way!

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QUESTION 1 of 3

Solve using the Chain Rule: -(x⁴-3)⁻²

y' = 8x³/(x⁴+4)³

y' = -8x³/(x⁴+3)³

y' = 4x³/(x⁴+3)³

QUESTION 1 of 3

RIGHT!

y' = 8x³/(x⁴+3)³

solutiony'=-2(-x⁴-3)⁻³(-4x³) y'=-2(-4x³) / (-x⁴-3)⁻³ y'=8x³ / (-x⁴-3)³ y'=-8x3 / (x⁴+3)³

NEXT QUESTION

QUESTION 2 of 3

Solve using the Chain Rule: y=³√(-2x⁴+5 )

-8x³/3³√(-2x⁴+5)²

-8x³/3³√(-2x⁴+10)²

-8x³/3³√(-3x⁴+5)²

QUESTION 2 of 3

RIGHT!

solutiony'=(-2x⁴+5)¹/³ y'=⅓(-2x⁴+5)⁻²/³(-8x³) y'=-8x³ / 3(-2x⁴+5)⁻²/³ y'=-8x³ /3 ³√(-2x⁴+5)²

NEXT QUESTION

QUESTION 3 of 3

Solve using the Chain Rule: y = (x³+3)⁵

10x²(x³+3)⁴

15x²(x³+3)⁴

15x²(x³+5)⁴

QUESTION 3 of 3

RIGHT!

solutiony'=5 (x³+3)⁴(3x²) y'=15x² (x³+3)⁴

NEXT QUESTION

QUESTION 4 to 8

Apply the differentiation rules in computing the derivative of an algebraic, exponential, and trigonometric functions

QUESTION 4 of 8

Solve the equation: y = sin2x³

y' = 6x²cosx³

y' = 6x²cos2x³

y' = 2x²cos2x³

QUESTION 4 of 8

RIGHT!

solutiony'=(cos2x³)(6x²) y'=6x²cos2x³

NEXT QUESTION

QUESTION 5 of 8

Solve the equation: y= sin³x⁵

y'= 15x⁴sin² x⁵secx⁵

y'= 15x⁴cos² x⁵cosx⁵

y'= 15x⁴tan² x⁵cosx⁵

QUESTION 5 of 8

RIGHT!

solutiony'=(3sin²x⁵)(cosx⁵)(5x⁴) y'=15x⁴sin²x⁵cosx⁵

See results

QUESTION 6 of 8

Solve the equation: y = tan5x³

10x²sec²5x³

-15x²sec²5x³

15x²sec²5x³

QUESTION 6 of 8

RIGHT!

solutiony'=(sec²5x³)(15x²) y'=15x²sec²5x³

See results

QUESTION 7 of 8

Solve the equation: y=sec4x^5

20x⁴sec5x⁵tan5x⁵

20x⁴sec4x⁵tan4x⁵

-20x⁴sec5x⁵tan4x⁵

QUESTION 7 of 8

RIGHT!

solutiony'=(sec4x⁵tan4x⁵)(20x⁴) y'=20x⁴sec4x⁵tan4x⁵

See results

QUESTION 8 of 8

Solve the equation: y=csc5x^5

-25x⁴csc5x⁵cot5x⁵

25x⁴csc5x⁴cot5x⁵

25x⁴csc5x⁴cot5x⁵

QUESTION 8 of 8

RIGHT!

solutiony'=(-csc5x⁵cot5x⁵)(25x⁴) y'=-25x⁴csc5x⁵cot5x⁵

See results

QUESTION 9 to 11

Integration using the Power Rule

QUESTION 9 of 11

Solve using the Power Rule -2x^-3dx

-1/x²+C

1/x²+C

1/x+C

QUESTION 9 of 11

RIGHT!

solution= (-2)(x⁻² / -2)+C =1x²+C

See results

QUESTION 10 of 11

Solve using the Power Rule (24x^5-10x)dx

4x⁶-10x²+C

-4x⁶+5x²+C

4x⁶-5x²+C

QUESTION 10 of 11

RIGHT!

solution(24)(x⁶/6)-(10)(x²/2)+C =4x⁶-5x²+C

See results

QUESTION 11 of 11

Solve using the Power Rule -35x^2/5/5dx

-2x⁷/⁵+C

2x⁷/⁵+C

-5x⁷/⁵+C

QUESTION 11 of 11

RIGHT!

solution =(-35/5)(x⁷/⁵ / 7/5) =-5x⁷/⁵+C

See results

QUESTION 12 to 15

Compute higher-order derivatives of functions

QUESTION 12 of 15

Compute the higher-order derivative of the function: y=-4x, find y’’

-4

QUESTION 12 of 15

RIGHT!

solution y’ = -4 y’’ = 0

See results

QUESTION 13 of 15

Compute the higher-order derivative of the function: y=5x^4, find y’’

60x

20x³

-60x

QUESTION 13 of 15

RIGHT!

solutiony’ = 20x3 y’’ = 60x

See results

QUESTION 14 of 15

Compute the higher-order derivative of the function: y=3x^5-2x, find y’’’

180x²

60x³

180³

QUESTION 14 of 15

RIGHT!

solutiony’ = 15x⁴ - 2 y’’ = 60x³ y’’’ = 180x²

See results

QUESTION 15 of 15

Compute the higher-order derivative of the function: y=4x^3, find y’’’

24x

12x²

24

QUESTION 15 of 15

RIGHT!

solutiony’ = 12x2 y’’ = 24x y’’’ = 24

See results

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REFERENCES

Department of Education. (2019). K to 12 BASIC EDUCATION CURRICULUM. https://www.deped.gov.ph/wp-content/uploads/2019/01/Basic-Calculus.pdf Free Printable Math Worksheets for Calculus. (n.d.). https://www.kutasoftware.com/freeica.html