What is implicit tan(5x+y)=5x ?

The answer to implicit tan(5x+y)=5x is (dy)/(dx)= 5/(sec^2(5x+y))-5

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implicit tan(5x+y)=5x

implicit derivative

tan (5 x + y) = 5 x

\frac{d y}{d x} = \frac{5}{sec ^{2} ( 5 x + y )} - 5

Solution steps

tan (5 x + y) = 5 x

Treat

y

y (x)

Differentiate both sides:

sec^{2} (5 x + y) (5 + \frac{d y}{d x}) = 5

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{5}{sec ^{2} ( 5 x + y )} - 5

\frac{d y}{d x} = \frac{5}{sec ^{2} ( 5 x + y )} - 5

y = x^{3}, [0, 4]

f (x) = \frac{x ^{2}}{( 2 + x )}

\int (x - 1)^{- 3} d x

e^{x}, e^{- x}, [- 2, 1]

\frac{d}{d x} (\frac{2 ( 1 + x ^{2} )}{( 1 - x ^{2} ) ^{2}})

What is implicit tan(5x+y)=5x ?
The answer to implicit tan(5x+y)=5x is (dy)/(dx)= 5/(sec^2(5x+y))-5