So i've tried everything...can u helP?! please?

Question

1. f(x)=x^2(x–7)^6 / (x^2+4)^7

2. f(x)=x^4cosh(x^3)

Can you find the derivative of these functions??

Answer 1

f(x)=x^2(x–7)^6 / (x^2+4)^7
f'(x= [ 2x (x-7)^6 (x^2+4)^7 + 6 x^2 (x-7)^5 (x^2+4)^7 - 14 x^3 (x-7)^6 (x^2+4) ^6 ] (x^2+4) ^14


f(x) = x^4 cosh (x^3)
f' (x) = 4 x^3 cosh( x^3) + x^4 3 x^2 sinh (x^3)
= 4 x^3 cosh (x^3) +3 x^6 sinh (x^3)

Answer 2

1, In problem 1, you have 3 separate functions of x. Lets call then U, V and W so
U=x, V=(x-7), and W=(x^2+4). Then we write,
f(UVW)= U^2 x V^6 / W^7
you will have to compute dU/dx=1 , dV/dx=1, and dW/dx= 2x.
The derivative of the numerator is 2UdU/dx (V^6) + 6V^5 dV/dx (U^2)
The derivitive of the denominator is -7 /W^8 dW/dx
Now substitute back in what U, V and W are and clean up the result.

In prob 2 you have to treat your term as the did the numerator in the previous problem. Look in the table of common derivitives to find the cosh function.

Answer 3

you must use the product rule and the quotient rule.