Differentiate (2^x)(5x^2+5x)^2.
This is a relatively difficult equation to differentiate as there are various parts to consider.Firstly, we will let u=2^x and v=(5x^2+5x)^2 in the product rule. Then the differential of u is (2^x)ln(2). We must remember how to differentiate exponential here where the exponent is a variable.Then the differential of v is 2(10x+5)(5x^2+5x) by using the chain rule. If we substitute the correct values into the product rule equation we get an answer of
2(2^x)(10x+5)(5x^2+5x)+(2^x)ln(2)(5x^2+5x)^2.
No need to simplify this.
GH
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