Find the derivatives of the following:tan (x + y) + tan (x – y) = x

Find the derivatives of the following:
tan (x + y) + tan (x – y) = x

योग

tan (x + y) + tan (x – y) = x

Differentiating with respect to x

`sec^2 (x + y) (1 + ("d"y)/("d"x)) + sec^2 (x - y) (1 - ("d"y)/("d"x))` = 1

`sec^2 (x + y) + sec^2 (x + y) ("d"y)/("d"x) + sec^2 (x - y) - sec^2 (x - y) ("d"y)/("d"x)` = 1

`[sec^2 (x + y) - sec^2 (x - y)] ("d"y)/("d"x) = 1 sec^2 (x + y) - sec^2 (x - y)`

`("d"y)/("d"x) = (1 - sec^2 (x + y) - sec^2 (x - y))/(se^2 (x + y) - sec^2 (x - y)`

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Differentiation Rules

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अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [पृष्ठ १७६]

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 8 | पृष्ठ १७६

Find the derivatives of the following functions with respect to corresponding independent variables:

y = (x² + 5) log(1 + x) e^–3x

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y = `root(3)(1 + x^3)`

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y = `"e"^sqrt(x)`

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h(t) = `("t" - 1/"t")^(3/2)`

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f(x) = `x/sqrt(7 - 3x)`

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y = (1 + cos²)⁶

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y = `"e"^(xcosx)`

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y = `sqrt(x + sqrt(x + sqrt(x)`

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y = `sin^-1 ((1 - x^2)/(1 + x^2))`

Find the derivatives of the following:

(cos x)^{log x}