Question

Y=4sin3x+x^8-6x y'-?

Answer 1

Y'=(4sin3x)'+(x⁸)'-(6x)'=12cos3x+8x⁷-6

Answer 2

To find the derivative of the given function y = 4sin(3x) + x^8 - 6x with respect to x, we'll first find the derivative of each term individually and then sum them up.

1. Derivative of 4sin(3x): The derivative of sin(3x) with respect to x is cos(3x), and since we have a coefficient of 4, the derivative of 4sin(3x) with respect to x is 4cos(3x).

2. Derivative of x^8: The power rule states that the derivative of x^n with respect to x is nx^(n-1). Applying this rule to x^8, we get the derivative as follows: d/dx (x^8) = 8x^(8-1) = 8*x^7.

3. Derivative of -6x: The derivative of -6x with respect to x is -6.

Now, summing up the derivatives of each term, we get the derivative of y with respect to x (y'):

y' = d/dx (4sin(3x) + x^8 - 6x) = 4 * cos(3x) + 8 * x^7 - 6.

So, the derivative of the given function y with respect to x is y' = 4cos(3x) + 8x^7 - 6.