Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = ex sin x
Advertisements
Solution
y = ex sin x
⇒ y = uv’ + vu’
Now u = ex
⇒ u’ = `("d"u)/("d"x) "e"^x`
v = sin x
⇒ v’ = `("d"v)/("d"x)` cos x
i.e. y’ = ex (cos x) + sin x (ex)
= ex [sin x + cos x]
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `(tanx - 1)/secx`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
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 = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
Choose the correct alternative:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
