If it is with respect to t: 1 If it is with respect to some other variable (x for example): (dt)/(dx), which is literally read "the derivative of t with respect to x"
Assume that the expression is: y = 9e^(t) Remember that the derivative of e^(t) with respect to t is e^(t). If we take the derivative of the function y, we have.. dy/dt = 9 d[e^(t)]/dt = 9e^(t) Note that I factor out the constant 9. If we keep the 9 in the brackets, then the solution doesn't make a difference.
d/dt cot (t) dt = - cosec2(t)
If x is a function of time, t, then the second derivative of x, with respect to t, is the acceleration in the x direction.
A dot A = A2 do a derivative of both sides derivative (A) dot A + A dot derivative(A) =0 2(derivative (A) dot A)=0 (derivative (A) dot A)=0 A * derivative (A) * cos (theta) =0 => theta =90 A and derivative (A) are perpendicular
The derivative of e7x is e7 or 7e.The derivative of e7x is 7e7xThe derivative of e7x is e7xln(7)
well if you're finding the derivative with respect to x, it would be -tx^(-t-1)
-t/(t-1)^2+1/(t-1)
No, the derivative of u with respect to v is not constant when t is held constant.
4e^t+cos(t)
Assume that the expression is: y = 9e^(t) Remember that the derivative of e^(t) with respect to t is e^(t). If we take the derivative of the function y, we have.. dy/dt = 9 d[e^(t)]/dt = 9e^(t) Note that I factor out the constant 9. If we keep the 9 in the brackets, then the solution doesn't make a difference.
d/dt cot (t) dt = - cosec2(t)
Suppose A is a vector with real components. A can be written as <f(t), g(t), h(t)>. Since the magnitude of A is constant we have f(t)*f(t) + g(t)*g(t) + h(t)*h(t) = c, where c is a non-negative real number. Take derivative of both sides of equation we get 2*f(t)*df(t)/dt + 2*g(t)*dg(t)/dt + 2*h(t)*dh(t)/dt = 0. Divide both sides by 2, we get f(t)*df(t)/dt + g(t)*dg(t)/dt + h(t)*dh(t)/dt = 0. Thus the dot product of A and its derivative is 0. This implies the angle between A and its derivative is Pi/2. Hence they are perpendicular.
T=theta so that it will not look so messy. g(T)=TcscT To find the first derivative, you must use the product rule. Product rule is derivative of the first times the second, plus the first times the derivative of the second, which will give you: g'(T)=0xcscT + Tx-cscTcotT, which simplifies: g'(T)= -cscTxcotT Now, take the derivative of that to get the second derivatice. In order to do that, you have to do the product rule again. g"(T)=(cscTcotT)cotT + -cscT(-csc^2T) {that's csc squared} which simplifies: g"(T)= cscTcot^2(T) + csc^3 (T)
Can you be more specific.
To find the instantaneous acceleration at t = 45.0s, you need to differentiate the velocity function with respect to time. The acceleration at t = 45.0s is the derivative of the velocity function at that time. Apply the derivative to the velocity function to find the acceleration at t = 45.0s.
The formula for instantaneous acceleration is given by the derivative of velocity with respect to time: a(t) = dv(t) / dt, where a(t) is the acceleration at time t and v(t) is the velocity at time t.
7/2 t^5/2^