Find the derivatives of the following:y = xcosx

Find the derivatives of the following:
y = `x^(cosx)`

Sum

y = `x^(cosx)`

Taking log on both sides

log y = log x^{cos x}

log y = cos x log x

Differentiating with respect to x

`1/y * ("d"y)/("d"x) = cosx xx 1/x + (logx)(- sinx)`

`1/y * ("d"y)/("d"x) = 1/x cos x - sin x * log x`

`("d"y)/("d"x) = y[cosx/x - sin x * log x]`

`("d"y)/("d"x) = x^(cosx) [cosx/x - sin x log x]`

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [Page 176]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 1 | Page 176

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

g(t) = 4 sec t + tan t

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

y = `sinx/x^2`

Differentiate the following:
y = tan 3x

Differentiate the following:
y = `"e"^sqrt(x)`

Differentiate the following:
y = 4 sec 5x

Differentiate the following:

y = `x"e"^(-x^2)`

Differentiate the following:

s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`

Differentiate the following:

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

Differentiate the following:

y = `(sin^2x)/cos x`

Differentiate the following:
y = (1 + cos²)⁶

Differentiate the following:

y = `"e"^(3x)/(1 + "e"^x`

Find the derivatives of the following:

(cos x)^{log x}