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y=f(a^x) and f(sinx)=lnx find dy/dx Solution) dy/dx = (a^x)(lnx)f''(a^x), .........(1) but f(sinx) = lnx implies f(x) = ln(arcsinx) hence f''(x) = (1/arcsinx) (1/ ( ( 1-x
A real estate agent makes a 1.5% commission on her sales. What is her commission if she sells a $359,000 house? Multiply $359,000 by the decimal equivalent of 1.5% (0.015) to ?
Definition: An equation is considered as function if for any x in the domain of the equation (the domain is the entire x's which can be plugged into the equation) the equation wil
Calculate average speed of a train: What is the average speed of a train which completes a 450-mile trip in 5 hours? Solution: Using Equation 15: V av = s/t V a
1) Find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2) Compute the work done by the force ?eld F(x,y,z) = x^2I + y j +y k in moving
For this point we've only looked as solving particular differential equations. Though, many "real life" situations are governed through a system of differential equations. See the
If we "break up" the root into the total of two pieces clearly we get different answers. Simplified radical form: We will simplify radicals shortly so we have to next
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Natural exponential function : There is a extremely important exponential function which arises naturally in several places. This function is called as the natural exponential fun
find or evaluate the integral integrate((e^2x + e^x + 1)/(e^x))dx
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