Differentiate and Simplify:
Find dy/dx: y = x7(2x+5)10
Please explain how you would solve this
+130118
y = (x)^7 * (2x + 5)^10
We want to use the product and chain rules, here...remember that if
y = u * v ......then y' = u' * v + u * v' where u, v are functions....so we have.....
dy / dx = 7(x)^6 * (2x + 5)^10 + (x)^7 * 10 * (2x + 5)^9 *(2)
Note that we used the chain rule in the last part [ in red ]
We can simplify thus.....factor out GCF of [ x^6 * ( 2x + 5)^9]
[ x^6 * ( 2x + 5)^9] * [ 7 (2x + 5) + 20x ]
[ x^6 * ( 2x + 5)^9] * [ 14x + 35 + 20x ]
[x^6 * (2x + 5)^9 ] * [ 34x + 35 ]
