Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = cos (a3 + x3)
उत्तर
y = cos (a3 + x3)
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
`("d"y)/("d"x) = - sin ("a"^3 + x^3) "d"/("d"x) ("a"^3 + x^3)`
`("d"y)/("d"x)` = – sin (a3 + x3)(0 + 3x2)
`("d"y)/("d"x)` = – 3x2 sin (a3 + x3)
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
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 = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
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 = tan 3x
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
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:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 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 = `1/("a" - z)`, then `("d"z)/("d"y)` is