Advertisements
Advertisements
Question
Differentiate the following:
y = tan 3x
Advertisements
Solution
y = tan 3x
Put u = 3x
`("d"u)/("d"x)` = 3
Now y = tan u
⇒ `("d"y)/("d"x)` = sec2u
So `("d"y)/("d"x) = ("d"y)/("d"u) xx ("d"u)/("d"x)` = (sec2 u)(3)
= 3 sec2 3x
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 = `(tanx - 1)/secx`
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
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
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:
y = `x^(cosx)`
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
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 y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a 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?
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
