What is (\partial)/(\partial x)(sin(x^4+y^3)) ?

The answer to (\partial)/(\partial x)(sin(x^4+y^3)) is cos(x^4+y^3)*4x^3

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(\partial)/(\partial x)(sin(x^4+y^3))

\frac{\partial}{\partial x} (sin (x^{4} + y^{3}))

cos (x^{4} + y^{3}) \cdot 4 x^{3}

Solution steps

\frac{\partial}{\partial x} (sin (x^{4} + y^{3}))

Treat

y

as a constant

Apply the chain rule:

cos (x^{4} + y^{3}) \frac{\partial}{\partial x} (x^{4} + y^{3})

= cos (x^{4} + y^{3}) \frac{\partial}{\partial x} (x^{4} + y^{3})

\frac{\partial}{\partial x} (x^{4} + y^{3}) = 4 x^{3}

= cos (x^{4} + y^{3}) \cdot 4 x^{3}

f (x) = x^{2} - 3, (4, 13)

x \to 0 + lim (\frac{7}{x} - \frac{7}{∣ x ∣})

\frac{d}{d x} (\frac{2}{1 + x ^{3}})

\frac{s ^{2}}{( s - 3 ) ^{2}}

2 + 5 x^{2} - 2 x^{3}

What is (\partial)/(\partial x)(sin(x^4+y^3)) ?
The answer to (\partial)/(\partial x)(sin(x^4+y^3)) is cos(x^4+y^3)*4x^3