Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = sin (ex)
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x – 3 sin x
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 = ex sin x
Differentiate the following:
y = tan 3x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
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:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
