"To find the derivative of the function x^4sin x, we can use the product rule. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by: \n d/dx(u(x)v(x)) = u'(x)v(x) + u(x)v'(x) Let's apply the product rule to the given function: \nStep 1: Identify u(x) and v(x): \n u(x) = x^4 and v(x) = sin x \nStep 2: Find u'(x) and v'(x): \n u'(x) = 4x^3 (using the power rule) \nv'(x) = cos x (derivative of sin x is cos x) \nStep 3: Apply the product rule: \nd/dx(x^4sin x) = u'(x)v(x) + u(x)v'(x) \n d/dx(x^4sin x) = 4x^3sin x + x^4cos x \n Therefore, the derivative of x^4sin x is 4x^3sin x + x^4cos x.
Below is my string.
"To find the derivative of the function x^4sin x, we can use the product rule. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by: \n d/dx(u(x)v(x)) = u'(x)v(x) + u(x)v'(x) Let's apply the product rule to the given function: \nStep 1: Identify u(x) and v(x): \n u(x) = x^4 and v(x) = sin x \nStep 2: Find u'(x) and v'(x): \n u'(x) = 4x^3 (using the power rule) \nv'(x) = cos x (derivative of sin x is cos x) \nStep 3: Apply the product rule: \nd/dx(x^4sin x) = u'(x)v(x) + u(x)v'(x) \n d/dx(x^4sin x) = 4x^3sin x + x^4cos x \n Therefore, the derivative of x^4sin x is 4x^3sin x + x^4cos x.