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.
sin (ax + b)
Differentiate the function with respect to x.
`sec(tan (sqrtx))`
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
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)`
Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0
If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
Let f(x)= |cosx|. Then, ______.
sinn (ax2 + bx + c)
sinx2 + sin2x + sin2(x2)
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.
`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to
If sin y = x sin (a + y), then value of dy/dx is
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 ______.
The set of all points where the function f(x) = x + |x| is differentiable, is ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
Differentiability determines whether a function has what at a particular point?
Which expression defines the derivative of a real function \[f\] at a point \[c\] in its domain?
What is \[\frac{d}{dx}(\sin x)\]?
What is \[\frac{d}{dx}(\cos x)\]?
What is \[\frac{d}{dx}(\tan x)\]?
Which limit is the left-hand derivative at \[x=c\]?
For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[b\]?
If \[f\] is differentiable at \[c\], which limit equals \[f'(c)\]?
For \[f(x)=|x|\], what is the right-hand derivative at \[x=0\]?
Why is \[|x|\] not differentiable at \[x=0\]?
What does differentiability at a point mean?
