Final Answer
Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=6^{-21x}$ and $g=\cos\left(2x^2\right)$
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$\frac{d}{dx}\left(6^{-21x}\right)\cos\left(2x^2\right)+6^{-21x}\frac{d}{dx}\left(\cos\left(2x^2\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 6^(-21x)cos(2x^2). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=6^{-21x} and g=\cos\left(2x^2\right). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.