質問: How do you find the derivative for #(-7x^2+8)^8(3x^2+9)^10#? ============================================================
回答: #\frac{dy}{dx}=-4x(189x^2+132)(-7x^2+8)^7(3x^2+9)^9# #### Explanation: Using product rule of differentiation as follows #\frac{d}{dx}(-7x^2+8)^8(3x^2+9)^10# #=(-7x^2+8)^8\frac{d}{dx}(3x^2+9)^10+(3x^2+9)^10\frac{d}{dx}(-7x^2+8)^8# #=(-7x^2+8)^8(10(3x^2+9)^9)\frac{d}{dx}(3x^2+9)+(3x^2+9)^10(8(-7x^2+8)^7)\frac{d}{dx}(-7x^2+8)# #=10(-7x^2+8)^8(3x^2+9)^9(6x)+8(3x^2+9)^10(-7x^2+8)^7\(-14x)# #=4x(-7x^2+8)^7(3x^2+9)^9(15(-7x^2+8)-28(3x^2+9))# #=4x(-7x^2+8)^7(3x^2+9)^9(-189x^2-132)# #=-4x(189x^2+132)(-7x^2+8)^7(3x^2+9)^9#