Find the derivative of $\frac{3\cdot 2\left(\frac{1+\sin\left(x\right)}{1-\sin\left(x\right)}\right)^2\cos\left(x\right)}{\left(1-\sin\left(x\right)\right)^2}$
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Learn how to solve differential calculus problems step by step online. Find the derivative of (3((1+sin(x))/(1-sin(x)))^2*2cos(x))/((1-sin(x))^2). Simplifying. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Multiplying the fraction by 6\cos\left(x\right). Divide fractions \frac{\frac{6\left(1+\sin\left(x\right)\right)^2\cos\left(x\right)}{\left(1-\sin\left(x\right)\right)^2}}{\left(1-\sin\left(x\right)\right)^2} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.
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The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.