Differentiate $$K ( x ) = \left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right)$$

question 63

Multiple Choice

Differentiate. $$K ( x ) = \left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right)$$

• A) \(15 x ^ { 4 } \left( x ^ { 6 } - 4 x \right) + \left( 3 x ^ { 5 } + 1 \right) \left( 6 x ^ { 5 } - 4 \right)\)
• B) \(\left( x ^ { 6 } - 4 x \right) + \left( 3 x ^ { 5 } + 1 \right)\)
• C) \(15 x ^ { 4 } \left( 6 x ^ { 5 } - 4 \right) + \left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right)\)
• D) \(15 x ^ { 4 } \left( 6 x ^ { 5 } \right) + \left( 3 x ^ { 5 } \right) \left( x ^ { 6 } - 4 x \right)\)
• E) \(\left( 3 x ^ { 5 } + 1 \right) \left( x ^ { 6 } - 4 x \right) + 15 x ^ { 4 } \left( 6 x ^ { 5 } - 4 \right) + 1\)

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Definitions:

Internal Rate

The interest rate at which the net present value of all the cash flows (both positive and negative) from a project or investment equals zero, used in capital budgeting to measure and compare the profitability of investments.

Nth-Order Equations

Equations that involve derivatives of an unknown function to the nth degree, often found in mathematics and physics.

Imaginary Solutions

Solutions to equations that include the square root of a negative number, often involving the imaginary unit 'i'.

Net Present Value

A financial metric that calculates the value of a series of cash flows by discounting them to the present day, taking into account the time value of money.