Final answer to the problem
$\frac{12x}{\mathrm{cosh}\left(6x^2\right)}+\frac{-72x^{3}\mathrm{sinh}\left(6x^2\right)}{\mathrm{cosh}\left(6x^2\right)^{2}}$
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Step-by-step Solution
Learn how to solve product rule of differentiation problems step by step online. Find the derivative of 6x^2cosh(6x^2)^(-1). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2 and g=\mathrm{cosh}\left(6x^2\right)^{-1}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Final answer to the problem
$\frac{12x}{\mathrm{cosh}\left(6x^2\right)}+\frac{-72x^{3}\mathrm{sinh}\left(6x^2\right)}{\mathrm{cosh}\left(6x^2\right)^{2}}$
