Question

if y = (sinx + cosx)secx then find dy/dx

Answer 1

Explanation:

y = sinxsecx + cosxsecx

y = sinx/cosx + cosx/cosx

y = tanx + 1

dy/dx = sec^2x

Answer 2

The value of $\frac{dy}{dx}$ is $sec^2x$.

Given:

y = (sinx + cosx)secx

To Find:

dy/dx of y.

Solution:

Given that,

y = (sinx + cosx)secx

Simplifying y:

y = sinx.secx + cosx.secx

We know that secx = $\frac{1}{cosx}$  therefore,

$y =$$\frac{sinx}{cosx} + \frac{cosx}{cosx}$

$y = tanx + 1$

Therefore,

$\frac{dy}{dx} = sec^2x + 0$

Therefore, $\frac{dy}{dx} = sec^2x$.

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