Advertisements
Advertisements
प्रश्न
Differentiate the function with respect to x:
sin3 x + cos6 x
Advertisements
उत्तर
Let, y = sin3 x + cos6 x
On differentiating with respect to x,
`dy/dx = d/dx sin^3 x + d/dx cos^6 x`
= `3 sin^2 x d/dx (sin x) + 6cos^5 x d/dx (cos x)`
= 3 sin2 x cos x + 6 cos5 x (−sin x)
= 3 sin2 x cos x − 6 cos5 x sin x
= 3 sin x cos x (sin x − 2 cos4 x)
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
cos (sin x)
Differentiate the function with respect to x.
sin (ax + b)
Differentiate the function with respect to x.
`cos (sqrtx)`
Prove that the function f given by f(x) = |x − 1|, x ∈ R is not differentiable at x = 1.
Differentiate the function with respect to x:
(3x2 – 9x + 5)9
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
If y = `[(f(x), g(x), h(x)),(l, m,n),(a,b,c)]`, prove that `dy/dx = |(f'(x), g'(x), h'(x)),(l,m, n),(a,b,c)|`.
Discuss the continuity and differentiability of the
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
If f(x) = x + 1, find `d/dx (fof) (x)`
If y = tan(x + y), find `("d"y)/("d"x)`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
Differential coefficient of sec (tan–1x) w.r.t. x is ______.
cos |x| is differentiable everywhere.
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
`cos(tan sqrt(x + 1))`
sinmx . cosnx
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
`tan^-1 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`
The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be
If `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
The function f(x) = x | x |, x ∈ R is differentiable ______.
If f(x) = | cos x |, then `f((3π)/4)` is ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
Which expression defines the derivative of a real function \[f\] at a point \[c\] in its domain?
If \[u\] and \[v\] are differentiable functions, what is \[(uv)'\]?
What is \[\frac{d}{dx}(\sin x)\]?
A function is differentiable at \[x=c\] when which condition holds?
What is the practical condition for differentiability at a point?
For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[b\]?
If \[f\] is differentiable at \[c\], which limit equals \[f'(c)\]?
Which conclusion establishes that \[f\] is continuous at \[x=c\]?
For \[f(x)=|x|\], what is the right-hand derivative at \[x=0\]?
When does a derivative exist?
