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The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if ${f(x) = \sin(x)}$, then ${f'(x) = \cos(x)\cdot D_x(x)}$
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$\frac{d}{dx}\left(\mathrm{sinh}\left(7x+5\right)\right)\cos\left(\mathrm{sinh}\left(7x+5\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of sin(sinh(7x+5)). The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. Taking the derivative of hyperbolic sine. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (5) is equal to zero.