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What is the antiderivative of 4 divided by x and why?
∫ 4/x dx= 4 ∫ 1/x dx= 4ln(x) + CThis is true for three reasons:the derivative of the term ln(x) is equal to 1/x4 is a constant factor of the term, and can be moved out of the integralC is an unknown constant, because we're looking at an indefinite integralYou can confirm this by taking the derivative of 4ln(x), which gives you 4/x, the original term.
What is the answer of the questions Differentiate X Squared and How?
Differentiating x^2 can be accomplished by using the Power Rule. This provides that d/dx (x^2)=2x
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))
Is term also means expression in algebra?
Generally expression is a collection of terms . In some cases , even a term may be considered as a expression .. e.g) "x+0" is a exp , "x" is term .. but we know both are equal.
What is an example of an exponential equation whose only solution is 4?
2^x = 16In general, "exponential" implies that the variable part is in the exponent. Write any equation with a power of 4, do the calculation, then replace "4" with "x".
How do you differentiate exp exp exp x?
By using the chain rule. Since the derivative of exp(x) is exp(x), the derivative of exp(exp(exp(x))) is exp(exp(exp(x))) times the derivative of what is inside the parentheses, i.e., exp(exp(exp(x))) times derivate of exp(exp(x)). Continue using the chain rule once more, for this expression.
How do you differentiate exp exp x?
Use the "chain rule" of differentiation: y=exp(exp(x)) taking ln both side in y=e x (1/y)dy/dx=e x dy/dx=y*e x dy/dx=exp(x+exp(x))
What is the antiderivative of exp -x?
It is -exp (-x) + C.
What is tanh?
tanh is the hyperbolic tangent and it is computed as sinh(x)/cosh(x) = [exp(x)-exp(-x)]/[exp(x)+exp(-x)] and there are other ways of computing it, including infinite series.
What is the antiderivative of 4 divided by x and why?
∫ 4/x dx= 4 ∫ 1/x dx= 4ln(x) + CThis is true for three reasons:the derivative of the term ln(x) is equal to 1/x4 is a constant factor of the term, and can be moved out of the integralC is an unknown constant, because we're looking at an indefinite integralYou can confirm this by taking the derivative of 4ln(x), which gives you 4/x, the original term.
What is the derivative of a half to the power of x?
(1/2)x = 2-x = exp (ln 2-x) = exp( -x ln 2). Since d/dx exp(x) = exp(x), we can use the chain rule to find that: d/dx (1/2)x = -(ln 2) exp(-x ln 2).
What is the derivative of half to the power of x?
(1/2)x = 2-x = exp (ln 2-x) = exp( -x ln 2). Since d/dx exp(x) = exp(x), we can use the chain rule to find that: d/dx (1/2)x = -(ln 2) exp(-x ln 2).
What is the derivative of -exp to the -x?
x e^x +C
Why are negative square roots are on the real number line if square root of a negative number not a real number?
Negative square roots are just the opposite of positive square roots. Since square roots (of positive numbers) are real, the negative square roots are also real.Square roots of negative numbers are not real.Note that -1 = exp(Pi*i), so (-1)^(1/2) = exp((1/2)*Pi*i) = i.Note that exp(i*x) = cos(x) + i*sin(x), for instance by taking derivatives:(d/dx)(exp(i*x)) = i*exp(i*x), and(d/dx)^2(exp(i*x)) =(-1)*exp(i*x).This means that the second derivative of exp(i*x) equals -exp(i*x).The same property holds for cos(x) + i*sin(x):(d/dx)(cos(x) + i*sin(x)) = -sin(x) + i*cos(x)(d/dx)^2(cos(x) + i*sin(x)) = -cos(x) - i*sin(x) = -(cos(x) + i*sin(x)))Hence cos(x) + i*sin(x)) = C + Dx + exp(i*x), for some C and D.Comparing the values on both sides for x = 0, we find:1 = C+1, so C = 0 and for the first derivative:i = D + i, so D = 0.So cos(x) + i*sin(x)) = exp(i*x) for all x.by comparing x=0 for both functions and their first derivative. Since they coincide,
How do you write exponential in scilab?
exp(x)
Differentiate sin x with respect to x?
cos x
How is xex and xe2x integrated manually?
The definite integral of the function f=x*exp(k*x) is (1/k)*(x-(1/k))*exp(k*x). So you have the answer to your questions by setting k equal to 1 then 2. I derived my formula by using integration by parts, setting u=x and dv=exp(k*x)dx.
