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f'[x] = lim(h->0) (f[x+h]-f[x])/h
lim(h->0) (sin[x+h]-sin[x])/h
By angle-addition formula, we have:
lim(h->0) (sin[x]cos[h]+sin[h]cos[x]-sin[x])/h
lim(h->0) (sin[x]cos[h]-sin[x])/h + lim(h->0) (sin[h]cos[x])/h
sin[x]*lim(h->0) (cos[h]-1)/h + cos[x]*lim(h->0) sin[h]/h
In a calculus class, it is shown that:
lim(h->0) (cos[h]-1)/h = 0 and that lim(h->0) sin[h]/h is 1. So,
sin[x]*lim(h->0) (cos[h]-1)/h + cos[x]*lim(h->0) sin[h]/h becomes
sin[x]*0 + cos[x]*1
cos[x]
So, if f[x] = sin[x], f'[x] = cos[x]
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What is the derivative of cos x sin x divided by cos x sin x?
(cos x sin x) / (cos x sin x) = 1. The derivative of a constant, such as 1, is zero.
What is the second derivitive of sec x?
Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
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(6 Cosx)2
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The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).
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The derivative of cos(x) is negative sin(x). Also, the derivative of sin(x) is cos(x).
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Every fourth derivative, you get back to "sin x" - in other words, the 84th derivative of "sin x" is also "sin x". From there, you need to take the derivative 3 more times, getting:85th derivative: cos x86th derivative: -sin x87th derivative: -cos x
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The derivative with respect to 'x' of sin(pi x) ispi cos(pi x)
What is the Derivative of sine ex?
The derivative of sin (x) is cos (x). It does not work the other way around, though. The derivative of cos (x) is -sin (x).
When does cos x equal -sin x?
The derivative of cos(x) equals -sin(x); therefore, the anti-derivative of -sin(x) equals cos(x).
What is the derivative of cos x sin x divided by cos x sin x?
(cos x sin x) / (cos x sin x) = 1. The derivative of a constant, such as 1, is zero.
How do you differentiate sin sin x?
To differentiate y=sin(sin(x)) you need to use the chain rule. A common way to remember the chain rule is "derivative of the outside, keep the inside, derivative of the inside". First, you take the derivative of the outside. The derivative of sin is cos. Then, you keep the inside, so you keep sin(x). Then, you multiple by the derivative of the inside. Again, the derivative of sinx is cosx. In the end, you get y'=cos(sin(x))cos(x))
What is the derivative of sqrt sin x?
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What is the second derivitive of sec x?
Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
What is the derivative of 6 sin x mutiply sin x?
(6 Cosx)2
Find derivative of sinx using first principle?
The derivative of sin(x) is cos(x).
How do you differentiate cosine square root of x?
The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).
