Please help! For the function f(x) = 2x^6 + 3x^4 - 4x^3 + (1/x) - sin(2x) find the first four derivatives.

Mathematics

1 answer:

klasskru [66]3 years ago

8 0

Answer:

See the explanation

Step-by-step explanation:

We know that

f(x) = 2x⁶ + 3x⁴ - 4x³ + (1/x) - sin2x

Lets calculate the derivatives:

f'(x) = 6(2x⁵) + 4(3x³) - 3(4x²) -( 1/x²) - 2(cos2x)

f'(x) = 12x⁵ + 12x³ - 12x² - (1/x²) - 2cos2x

Similarly:

f''(x) = 60x⁴ + 36x² - 24x + (2/x³) + 4sin2x

f'''(x) = 240x³ + 72x - 24 - (6/x⁴) + 8cos2x

Rearrange:

f'''(x) - 240x³ +72x - (6/x⁴) + 8cos2x - 24

f''''(x) = 720x² + 72 + (24/x⁵) - 16sin2x

Rearrange:

f''''(x) = 720x² + (24/x⁵) - 16sin2x +72

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stellarik [79]

Remember you can do anything to an equation as long asyou do it to both sides

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3 0

4 years ago

Could someone please help me answer questions 2,3 & 4. Please show your workings.

kirill [66]

1)
x^2 -5x + 4 = 0
(x -4)(x - 1) = 0
x - 4 = 0; x = 4
x - 1 = 0; x = 1
answer
x = 1 and x =4

2)
x^2 -7x + 12 = 0
(x-3)(x-4) = 0
x - 3 = 0; x = 3
x - 4 = 0; x = 4
answer
x = 3 and x =4

3)
x^2 + 7x + 6 = 12x
x^2 - 5x + 6 = 0
(x - 3)(x - 2) = 0
x - 3 = 0; x = 3
x - 2 = 0; x = 2
answer
x = 3 and x = 2

4)
15 + 2x = x^2
x^2 - 2x - 15 = 0
(x - 5)(x+ 3) = 0
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answer
x = -3 and x = 5

8 0

4 years ago

Please help and explain

sveticcg [70]

Answer:

x = 71

Step-by-step explanation:

Since the 2 legs are congruent ( both 21 ) then the triangle is isosceles.

Thus the base angles are congruent, then

x = $\frac{180-38}{2}$ = $\frac{142}{2}$ = 71