Solve p= 3a-b^2a-b^3a b^5b-a

Question

Function

Find the first partial derivative with respect to a

Find the first partial derivative with respect to b

\frac{\partial p}{\partial a} = 2 - b^{2} - b^{9}

Evaluate

p = 3 a - b^{2} a - b^{3} a b^{5} \times b - a

Simplify

More Steps

Evaluate

3 a - b^{2} a - b^{3} a b^{5} \times b - a

Multiply

More Steps

Multiply the terms

- b^{3} a b^{5} \times b

Multiply the terms with the same base by adding their exponents

- b^{3 + 5 + 1} a

Add the numbers

- b^{9} a

3 a - b^{2} a - b^{9} a - a

Subtract the terms

More Steps

Evaluate

3 a - a

Collect like terms by calculating the sum or difference of their coefficients

(3 - 1) a

Subtract the numbers

2 a

2 a - b^{2} a - b^{9} a

p = 2 a - b^{2} a - b^{9} a

Find the first partial derivative by treating the variable b as a constant and differentiating with respect to a

\frac{\partial p}{\partial a} = \frac{\partial}{\partial a} (2 a - b^{2} a - b^{9} a)

Use differentiation rule \frac{\partial}{\partial x} (f (x) \pm g (x)) = \frac{\partial}{\partial x} (f (x)) \pm \frac{\partial}{\partial x} (g (x))

\frac{\partial p}{\partial a} = \frac{\partial}{\partial a} (2 a) - \frac{\partial}{\partial a} (b^{2} a) - \frac{\partial}{\partial a} (b^{9} a)

Evaluate

More Steps

Evaluate

\frac{\partial}{\partial a} (2 a)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

2 \times \frac{\partial}{\partial a} (a)

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

2 \times 1

Multiply the terms

2

\frac{\partial p}{\partial a} = 2 - \frac{\partial}{\partial a} (b^{2} a) - \frac{\partial}{\partial a} (b^{9} a)

Evaluate

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Evaluate

\frac{\partial}{\partial a} (b^{2} a)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

b^{2} \times \frac{\partial}{\partial a} (a)

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

b^{2} \times 1

Multiply the terms

b^{2}

\frac{\partial p}{\partial a} = 2 - b^{2} - \frac{\partial}{\partial a} (b^{9} a)

Solution

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Evaluate

\frac{\partial}{\partial a} (b^{9} a)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

b^{9} \times \frac{\partial}{\partial a} (a)

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

b^{9} \times 1

Multiply the terms

b^{9}

\frac{\partial p}{\partial a} = 2 - b^{2} - b^{9}

Show Solution

Solve the equation

Solve for a

Solve for p

a = \frac{p}{2 - b ^{2} - b ^{9}}

Evaluate

p = 3 a - b^{2} a - b^{3} a b^{5} \times b - a

Simplify

More Steps

Evaluate

3 a - b^{2} a - b^{3} a b^{5} \times b - a

Multiply

More Steps

Multiply the terms

- b^{3} a b^{5} \times b

Multiply the terms with the same base by adding their exponents

- b^{3 + 5 + 1} a

Add the numbers

- b^{9} a

3 a - b^{2} a - b^{9} a - a

Subtract the terms

More Steps

Evaluate

3 a - a

Collect like terms by calculating the sum or difference of their coefficients

(3 - 1) a

Subtract the numbers

2 a

2 a - b^{2} a - b^{9} a

p = 2 a - b^{2} a - b^{9} a

Swap the sides of the equation

2 a - b^{2} a - b^{9} a = p

Collect like terms by calculating the sum or difference of their coefficients

(2 - b^{2} - b^{9}) a = p

Divide both sides

\frac{( 2 - b ^{2} - b ^{9} ) a}{2 - b ^{2} - b ^{9}} = \frac{p}{2 - b ^{2} - b ^{9}}

Solution

a = \frac{p}{2 - b ^{2} - b ^{9}}

Show Solution