How do you differentiate f(x)=(2x^3)(cos^2x^2) using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer IZUkuABA Jun 26, 2018 2x^3*2*cosx^2*-sin(x)^2*2x+cos^2x^2*6x^2 Explanation: we have f(x)=(2x^3)(cos^2x^2) dy/dx=2x^3*d(cos^2x^2)/dx+(cos^2x^2)*d(2x^3)/dx =>2x^3*2*d(cosx^2)/dx+(cos^2x^2)*2*3*x^2.....using[dy/dx=x^n=>nx^(n-1)] =>2x^3*2*(cosx^2)*-sind(x^2)/dx+(cos^2x^2)*6*x^2 .........using [dy/dx=cosx=>-sinx] =>2x^3*2*(cosx^2)*-sinx^2*2x+(cos^2x^2)*6*x^2 Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of f(x) = (x - 3)(2 - 3x)(5 - x) ? How do you use the product rule to find the derivative of y=x^2*sin(x) ? How do you use the product rule to differentiate y=cos(x)*sin(x) ? How do you apply the product rule repeatedly to find the derivative of f(x) = (x^4 +x)*e^x*tan(x) ? How do you use the product rule to find the derivative of y=(x^3+2x)*e^x ? How do you use the product rule to find the derivative of y=sqrt(x)*cos(x) ? How do you use the product rule to find the derivative of y=(1/x^2-3/x^4)*(x+5x^3) ? How do you use the product rule to find the derivative of y=sqrt(x)*e^x ? How do you use the product rule to find the derivative of y=x*ln(x) ? See all questions in Product Rule Impact of this question 1711 views around the world You can reuse this answer Creative Commons License