What is implicit (dy)/(dx),x^8+y^7=5 ?

The answer to implicit (dy)/(dx),x^8+y^7=5 is (dy)/(dx)=-(8x^7)/(7y^6)

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implicit (dy)/(dx),x^8+y^7=5

implicit derivative

\frac{d y}{d x}, x^{8} + y^{7} = 5

\frac{d y}{d x} = - \frac{8 x ^{7}}{7 y ^{6}}

Solution steps

x^{8} + y^{7} = 5

Treat

y

y (x)

Differentiate both sides:

8 x^{7} + 7 y^{6} \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{8 x ^{7}}{7 y ^{6}}

\frac{d y}{d x} = - \frac{8 x ^{7}}{7 y ^{6}}

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\int \frac{3 t ^{4} - t ^{3} + 6 t ^{2}}{t ^{4}} d t

csc (y) d x + sec^{2} (x) d y = 0

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What is implicit (dy)/(dx),x^8+y^7=5 ?
The answer to implicit (dy)/(dx),x^8+y^7=5 is (dy)/(dx)=-(8x^7)/(7y^6)