Advertisements
Advertisements
Question
Differentiate the following:
y = sin (ex)
Advertisements
Solution
y = sin (ex)
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
y = `cos ("e"^x) * "d"/("d"x) ("e"^x)`
y = cos ((ex)) . ex
y = ex cos (ex)
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = cos (tan x)
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
Find the derivatives of the following:
If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ
Choose the correct alternative:
If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
