What is implicit (dy)/(dx),sec(9x+2)+6y^2=42 ?

The answer to implicit (dy)/(dx),sec(9x+2)+6y^2=42 is (dy)/(dx)=-(3sec(9x+2)tan(9x+2))/(4y)

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implicit (dy)/(dx),sec(9x+2)+6y^2=42

implicit derivative

\frac{d y}{d x}, sec (9 x + 2) + 6 y^{2} = 42

\frac{d y}{d x} = - \frac{3 sec ( 9 x + 2 ) tan ( 9 x + 2 )}{4 y}

Solution steps

sec (9 x + 2) + 6 y^{2} = 42

Treat

y

y (x)

Differentiate both sides:

sec (9 x + 2) tan (9 x + 2) \cdot 9 + 12 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{3 sec ( 9 x + 2 ) tan ( 9 x + 2 )}{4 y}

\frac{d y}{d x} = - \frac{3 sec ( 9 x + 2 ) tan ( 9 x + 2 )}{4 y}

t an g e n t f (x) = 3 x^{3} - x^{2} + 4, at x = 1

\frac{d}{d x} (e^{4 x^{2}} csc (5 x))

d er i v a t i v e sin (- 2 x)

\int \frac{1}{10 ( x ^{2} + 1 )} d x

d er i v a t i v e (2 x - 7)^{- 1} (x + 5)

What is implicit (dy)/(dx),sec(9x+2)+6y^2=42 ?
The answer to implicit (dy)/(dx),sec(9x+2)+6y^2=42 is (dy)/(dx)=-(3sec(9x+2)tan(9x+2))/(4y)