Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = tan θ (sin θ + cos θ)
Advertisements
Solution
y = tan θ (sin θ + cos θ)
`("d"y)/("d"x)` = tan θ (cos θ – sin θ) + (sin θ + cos 0) sec2 θ
= tan θ cos θ – tan θ sin θ + sin θ sec2θ + cos θ sec2θ
= `tan theta cos theta - tan theta sin theta + sintheta/(cos^2theta) + costheta/(cos^2theta)`
= `sin theta/cos theta cos theta - sin theta/cos theta sin theta + sin theta/cos theta * 1/cos theta + 1/costheta`
= sin θ – sin2θ sec θ + tan θ sec θ + sec θ
= sin θ + (1 – sin2θ) sec θ + sec θ tan θ
= `sin theta + cos^2theta xx 1/cos theta + sectheta tan theta`
= sin θ + cos θ + sec θ tan θ
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Find the derivatives of the following functions with respect to corresponding independent variables:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = e–mx
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/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:
x = `"a" cos^3"t"` ; y = `"a" sin^3"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:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Find the derivatives of the following:
If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`
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:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
