tentukan turunan total f(x,y) = 5x^5 + 4x^4y - 3x^3 2y^2 - 2x^22y^3 + xy^4 + 7y^5
Answer (4)
1 + 2 + 3 + 4 + 5 + ⋯ + 50 1 ; 2 ; 3 ; 4 ; 5 ; … ; 50 a re t h e t er m s o f a a r i t hm e t i c se q u e n ce w h ere a 1 = 1 an d d = 1 S u m : S n = 2 a 1 + a n ⋅ n S 50 = 2 1 + 50 ⋅ 50 = 51 ⋅ 25 = 1275 ← so l u t i o n
Look at the first one and the last one: 1 + 50 = 51 Look at the second one and the second-last one: 2 + 49 = 51 Look at the third one and the third-last one: 3 + 48 = 51
Every pair you construct in this way adds up to 51 .
There are ( 50/2 ) = 25 pairs.
They all add up to ( 25 pairs ) x ( 51 per pair ) = 1,275
The sum of the first 50 natural numbers is 1275, calculated using the formula S n = 2 n ⋅ ( a 1 + a n ) , where n is the number of terms. This allows for a quick calculation without adding all numbers individually. Using this formula, we find S 50 = 1275 .
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Jawab:Penjelasan dengan langkah-langkah:The total derivative of the function f(x,y) = 5x⁵ + 4x⁴y - 3x³(2y²) - 2x²(2y³) + xy⁴ + 7y⁵ is df = (25x⁴ + 16x³y - 18x²y² - 8x²y³ + y⁴)dx + (4x⁴ - 12x³y - 12x²y² + 4xy³ + 35y⁴)dy.To find the total derivative, we need to calculate the partial derivatives of f with respect to x and y, and then combine them using the formula: df = (∂f/∂x)dx + (∂f/∂y)dy.First, let's find the partial derivative with respect to x:∂f/∂x = 25x⁴ + 16x³y - 18x²y² - 8x²y³ + y⁴Next, let's find the partial derivative with respect to y:∂f/∂y = 4x⁴ - 12x³y - 12x²y² + 4xy³ + 35y⁴Now, we can plug these into the formula for the total derivative:df = (25x⁴ + 16x³y - 18x²y² - 8x²y³ + y⁴)dx + (4x⁴ - 12x³y - 12x²y² + 4xy³ + 35y⁴)dy
