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Step-by-step Solution

Derive the function $\left(2\sin\left(x\right)-1\cdot 3\cos\left(x\right)\right)^3$ with respect to x

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Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\left(2\sin\left(x\right)-1\cdot 3\cdot \cos\left(x\right)\right)^3\right)$

Learn how to solve differential calculus problems step by step online.

$3\left(2\sin\left(x\right)-3\cos\left(x\right)\right)^{2}\frac{d}{dx}\left(2\sin\left(x\right)-3\cos\left(x\right)\right)$

Unlock this full step-by-step solution!

Learn how to solve differential calculus problems step by step online. Derive the function (2sin(x)-*3*cos(x))^3 with respect to x. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Expand \left(2\sin\left(x\right)-3\cos\left(x\right)\right)^{2}. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.

Answer

$3\left(4\sin\left(x\right)^2-12\sin\left(x\right)\cos\left(x\right)+9\cos\left(x\right)^2\right)\left(2\cos\left(x\right)+3\sin\left(x\right)\right)$

Problem Analysis

$\frac{d}{dx}\left(\left(2\sin\left(x\right)-1\cdot 3\cdot \cos\left(x\right)\right)^3\right)$

Main topic:

Differential calculus

Related formulas:

5. See formulas

Time to solve it:

~ 1.32 seconds