Question

derivative of d/dx of secx.cosecx​

Answer 1

Step-by-step explanation:

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Answer 2

The derivative is, $\frac{cos2x}{(sinx.cosx)^{2} }$.

• Apart from integration, differentiation is one of the two key ideas of calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation.
• A function's derivative is the definition of a function's rate of change at a specific point.

Here, according to the given information, we need to evaluate the derivate of, $y = secx.cosecx$.

Now, by differentiating, we get,

$\frac{dy}{dx} = secx\frac{d}{dx} (cosecx)+cosecx{d}{dx}(secx)$

$=secx(-cosecxcotx)+cosecx(secxtanx)\\=-\frac{1}{sin^{2} x} +\frac{1}{cos^{2}x} \\=\frac{cos2x}{(sinx.cosx)^{2} }$

Hence, the derivative is, $\frac{cos2x}{(sinx.cosx)^{2} }$.

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