Question

Find the derivative of the given function
y=-x²/16+2/x-x³ / 2+1/3 x²+x/3

Answer 1

To find the derivative of the given function, we apply the rules of differentiation. We break down the function into the numerator and the denominator, differentiate each part, and simplify the result.

Step-by-step explanation:

To find the derivative of the given function, we need to apply the rules of differentiation. Let's break down the given function step by step:

• Start by finding the derivative of the numerator: -x²/16 + 2/x - x³
• The derivative of -x²/16 is (-2x)/16 = -x/8
• The derivative of 2/x is -2/x²
• The derivative of -x³ is -3x²
• Now, let's find the derivative of the denominator: 2 + (1/3)x² + (1/3)x
• The derivative of 2 is 0
• The derivative of (1/3)x² is (2/3)x
• The derivative of (1/3)x is 1/3
• Finally, let's simplify the derivative by dividing the numerator by the denominator.

Combining all the derivatives, we get:

(-x/8 - 2/x² - 3x²) / (2 + (2/3)x + (1/3)x²)

That is the derivative of the given function.