Answer
$y'=2x^{2}\cosh(x^{2})+\sinh(x^{2})$
Work Step by Step
$y=x\sinh(x^{2})$
Start the differentiation process by using the product rule:
$y'=x[\sinh(x^{2})]'+(x)'\sinh(x^{2})=...$
Use the chain rule to evaluate the indicated derivatives:
$...=x(x^{2})'\cosh(x^{2})+\sinh(x^{2})=...$
$...=(x)(2x)\cosh(x^{2})+\sinh(x^{2})=...$
$...=2x^{2}\cosh(x^{2})+\sinh(x^{2})$
