Find the derivative of $5\tan\left(2x\right)^5\left(\frac{\sin\left(2\right)}{\cos\left(2\right)}\right)$

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$\frac{d}{dx}\left(-10.92519\tan\left(2x\right)^5\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of 5tan(2x)^5(sin(2)/(cos(2). Simplifying. The derivative of a function multiplied by a constant (-10.92519) 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}. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}.