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Popular >

derivative of 9x^3y^5

Solution

\frac{d}{d x} (9 x^{3} y^{5})

Solution

9 (3 x^{2} y^{5} + 5 y^{4} \frac{d y}{d x} x^{3})

Solution steps

\frac{d}{d x} (9 x^{3} y^{5})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (x^{3} y^{5})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = y^{5}

= 9 (\frac{d}{d x} (x^{3}) y^{5} + \frac{d}{d x} (y^{5}) x^{3})

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

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

= 9 (3 x^{2} y^{5} + 5 y^{4} \frac{d y}{d x} x^{3})

Popular Examples

extreme f(x)=6y^2+4x^2-12xy-4y extreme points

f (x) = 6 y^{2} + 4 x^{2} - 12 x y - 4 y

extreme f(x)=x^3+4x^2-3x+6 extreme points

f (x) = x^{3} + 4 x^{2} - 3 x + 6

extreme f(x,y)=x^3+y^3+2x^2+4y^2+6 extreme points

f (x, y) = x^{3} + y^{3} + 2 x^{2} + 4 y^{2} + 6

extreme f(x)=3x^2-18x+23 extreme points

f (x) = 3 x^{2} - 18 x + 23

extreme f(x,y)=5+3x^2+3y^2+2y^3+x^3 extreme points

f (x, y) = 5 + 3 x^{2} + 3 y^{2} + 2 y^{3} + x^{3}

Frequently Asked Questions (FAQ)

What is the derivative of 9x^3y^5 ?
The derivative of 9x^3y^5 is 9(3x^2y^5+5y^4(dy)/(dx)x^3)
What is the first derivative of 9x^3y^5 ?
The first derivative of 9x^3y^5 is 9(3x^2y^5+5y^4(dy)/(dx)x^3)