If y=2x7+4x6−3x4+12𝑦=2𝑥7+4𝑥6−3𝑥4+12, find dydx.

To find the derivative of the function y = 2x^7 + 4x^6 - 3x^4 + 12 with respect to x, we apply the power rule, which states that the derivative of x^n is n*x^(n-1).

Step 1: Differentiate 2x^7 The derivative of 2x^7 is 7*2x^(7-1) = 14x^6.

Step 2: Differentiate 4x^6 The derivative of 4x^6 is 6*4x^(6-1) = 24x^5.

Step 3: Differentiate -3x^4 The derivative of -3x^4 is 4*(-3)x^(4-1) = -12x^3.

Step 4: Differentiate 12 The derivative of a constant is 0, so the derivative of 12 is 0.

Step 5: Combine the results The derivative of the function y = 2x^7 + 4x^6 - 3x^4 + 12 is dy/dx = 14x^6 + 24x^5 - 12x^3.

To find the derivative of the function y = 2x^7 + 4x^6 - 3x^4 + 12 with respect to x, we apply the power rule, which states that the derivative of x^n is n*x^(n-1).

The derivative of 2x^7 is 72x^(7-1) = 14x^6. The derivative of 4x^6 is 64x^(6-1) = 24x^5. The derivative of -3x^4 is 4*-3x^(4-1) = -12x^3. The derivative of a constant, like 12,