2 Calculus problems - i need help :S (1 Viewer)

[C6H12O6-Glucose]

(1)
find y' where,
e^(x^6*y) = x+y

(2)
Evaluate the following integral:
\int_{0}^{1} 7^t dt
thanks heaps

 

[Trebla]

(1)
find y' where,
e^(x^6*y) = x+y

(2)
Evaluate the following integral:
\int_{0}^{1} 7^t dt
thanks heaps

For the first one, use implicit differentiation
e^x6y = x + y
6x⁵e^x6y+e^x6ydy/dx = 1 + dy/dx
dy/dx = (6x⁵e^x6y - 1)/(1 - e^x6y)

For the second one, rewrite 7^t as e^{ln 7t} = e^{t ln 7}, thus