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.
`sec(tan (sqrtx))`
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Prove that the function f given by f(x) = |x − 1|, x ∈ R is not differentiable at x = 1.
If (x – a)2 + (y – b)2 = c2, for some c > 0, prove that `[1+ (dy/dx)^2]^(3/2)/((d^2y)/dx^2)` is a constant independent of a and b.
If f(x) = |x|3, show that f"(x) exists for all real x and find it.
If y = tan(x + y), find `("d"y)/("d"x)`
Differential coefficient of sec (tan–1x) w.r.t. x is ______.
`sin^-1 1/sqrt(x + 1)`
(sin x)cosx
sinmx . cosnx
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (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))`
Let c, k ∈ R. If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ... + f(20))| is equal to ______.
If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
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.
If \[u\] and \[v\] are differentiable functions, which formula is correct?
What is \[\frac{d}{dx}(\sin x)\]?
What is \[\frac{d}{dx}(\cos x)\]?
Which limit is the left-hand derivative at \[x=c\]?
When is a function differentiable on an open interval \[(a,b)\]?
If a function \[f\] is differentiable at a point \[c\], what must be true at that point?
If \[f\] is differentiable at \[c\], which limit equals \[f'(c)\]?
Which conclusion establishes that \[f\] is continuous at \[x=c\]?
When does a derivative exist?
