I need two examples

I need two examples

F = P(1 + r/100)^t Assume P and r are constant, find dF/dt.

Also find the solutions which satisfy y=1 when t=0 and y=0 when t=1 and sketch them on the same axes.

d/dt 83∫t (sec(29x+3)) dx= On what interval is the derivative defined?

d/dx 0∫9x^2 ((t*dt)/(t+3))

d/dx 0∫12x (cos^5 t)dt

A large snowball is melting so that it's radius is decreasing at the rate of 2 inches per hour. How fast is the volume decreasing at the moment that the radius is 3inches? HINT: volume of a sphere...

A street lamp 20' high creates a shadow of an owl. The owl is descending to a mouse vertically below. When the stationary mouse is 10' from the foot of the lamp, the owl is 15' vertically above and...

this question had several parts 1)Why can't we use the product rule to compute f'(0) My initial thought was that you cannot use the product rule t because sinx and 3√...

find dy/dx where y=2^(x/lnx)

Can you please explain step by step how to do it and the final result? Thanks!

We have done this problem writing in terms of sin3x and cos3x, but never sin2x and cos2x when the equation has 3x. This is a super important problem for extra credit and I don't understand how to...

We have done this problem writing in terms of sin3x and cos3x, but never sin2x and cos2x when the equation has 3x. This is a super important problem for extra credit and I don't understand...

Calculus I, Derivative t>=0

In Calculus, are any number to the power of x treated as E^x when working with derivatives? (i.e. 10^x ... 10xln(10)

Find the function of the form f(x)=a+bcos(cx) that is tangent to the line y=1 at the point (0,1), and tangent to the line y = x + (3/2) - (pi/4) at the point (pi/4, 3/2).

y=(xy)x Write an expression for dy/dx

Application of Derivatives

1. Find the equation of the line tangent to the curve 𝑦 = 1 √𝑥2+2 at 𝑥 = −1. Do not use the derivatives rules. Use the limit definition to calculate the derivative. [5 marks] need solution...

find equation of tangent line and normal line given x2/25 + y2/9 = 1 with coordinates (5sqrt(2)/2, 3sqrt(2)/2)

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