Question

Find all the derivatives of the function defined by f(x) = 8x^4 + 5x^3 - x^2 + 7

Answer 1

Answer:

First derivative:

• d(8x⁴ + 5x³ - x² + 7)

• d(8x⁴) + d(5x³) - d(x²) + d(7)

• 8d(x⁴) + 5d(x³) - d(x²) + 0
• 8*4x³ + 5*3x² - 2x
• Answer: 32x³ + 15x² - 2x

Second derivative:

• d(32x³ + 15x² - 2x)
• d(32x³) + d(15x²) - d(2x)
• 32d(x³) + 15d(x²) - 2d(x)
• 32*3x² + 15*2x - 2
• Answer: 96x² + 30x - 2

Third derivative:

• d(96x² + 30x - 2)

• d(96x²) + d(30x) - d(2)

• 96d(x²) + 30d(x) - 0
• 96*2x + 30
• Answer: 196x + 30

Fourth derivative:

• d(196x + 30)

• d(196x) + d(30)

• 196d(x) + 0
• Answer: 196

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