What is the derivative of 7x^3y^2+34x^2y^5 ?

The derivative of 7x^3y^2+34x^2y^5 is 7(3x^2y^2+2y(dy)/(dx)x^3)+34(2xy^5+5y^4(dy)/(dx)x^2)

What is the first derivative of 7x^3y^2+34x^2y^5 ?

The first derivative of 7x^3y^2+34x^2y^5 is 7(3x^2y^2+2y(dy)/(dx)x^3)+34(2xy^5+5y^4(dy)/(dx)x^2)

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\frac{d}{d x} (7 x^{3} y^{2} + 34 x^{2} y^{5})

7 (3 x^{2} y^{2} + 2 y \frac{d y}{d x} x^{3}) + 34 (2 x y^{5} + 5 y^{4} \frac{d y}{d x} x^{2})

Solution steps

\frac{d}{d x} (7 x^{3} y^{2} + 34 x^{2} y^{5})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x^{3} y^{2}) + \frac{d}{d x} (34 x^{2} y^{5})

\frac{d}{d x} (7 x^{3} y^{2}) = 7 (3 x^{2} y^{2} + 2 y \frac{d y}{d x} x^{3})

\frac{d}{d x} (34 x^{2} y^{5}) = 34 (2 x y^{5} + 5 y^{4} \frac{d y}{d x} x^{2})

= 7 (3 x^{2} y^{2} + 2 y \frac{d y}{d x} x^{3}) + 34 (2 x y^{5} + 5 y^{4} \frac{d y}{d x} x^{2})

f (x) = 7 x^{9} - 9 x^{7} - 7, - 3 \leq x \leq 3

f (x) = \frac{e ^{x}}{3 + e ^{x}}

f (x) = 8 x^{3} - x^{4}

f (x) = x^{3} - 27

g (x) = x^{2} + 2

What is the derivative of 7x^3y^2+34x^2y^5 ?
The derivative of 7x^3y^2+34x^2y^5 is 7(3x^2y^2+2y(dy)/(dx)x^3)+34(2xy^5+5y^4(dy)/(dx)x^2)
What is the first derivative of 7x^3y^2+34x^2y^5 ?
The first derivative of 7x^3y^2+34x^2y^5 is 7(3x^2y^2+2y(dy)/(dx)x^3)+34(2xy^5+5y^4(dy)/(dx)x^2)