Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Advertisements
उत्तर
tan (x + y) + tan (x – y) = x
Differentiating with respect to x
`sec^2 (x + y) (1 + ("d"y)/("d"x)) + sec^2 (x - y) (1 - ("d"y)/("d"x))` = 1
`sec^2 (x + y) + sec^2 (x + y) ("d"y)/("d"x) + sec^2 (x - y) - sec^2 (x - y) ("d"y)/("d"x)` = 1
`[sec^2 (x + y) - sec^2 (x - y)] ("d"y)/("d"x) = 1 sec^2 (x + y) - sec^2 (x - y)`
`("d"y)/("d"x) = (1 - sec^2 (x + y) - sec^2 (x - y))/(se^2 (x + y) - sec^2 (x - y)`
APPEARS IN
संबंधित प्रश्न
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 = ex 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 = `sinx/x^2`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = x sin x cos x
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 = sin x0
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = e–mx
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Choose the correct alternative:
If y = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
Choose the correct alternative:
If f(x) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
