Question

Find the derivative of the given function.
y=4x² (5-7x)^8

Answer 1

To find the derivative of the given function, we will use the product rule and the chain rule of differentiation.

Let u = 4x² and v = (5-7x)^8. Then, we have:

y = u * v

Using the product rule, we have:

y' = u' * v + u * v'

To find u' and v', we use the power rule and the chain rule:

u' = d/dx (4x²) = 8x

v' = d/dx (5-7x)^8 = 8(5-7x)^7 * (-7)

Now, we can substitute these values into the product rule formula:

y' = u' * v + u * v'

= 8x * (5-7x)^8 + 4x² * 8(5-7x)^7 * (-7)

Simplifying this expression, we get:

y' = 8x(5-7x)^7 * (40-56x-28x+49x)

= 8x(5-7x)^7 * (-14x+40)

Therefore, the derivative of the function y = 4x² (5-7x)^8 is y' = 8x(5-7x)^7 * (-14x+40).