Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to b
Find the first partial derivative with respect to c
∂b∂a=10b4c
Simplify
a=2b5c
Find the first partial derivative by treating the variable c as a constant and differentiating with respect to b
∂b∂a=∂b∂(2b5c)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂b∂a=2c×∂b∂(b5)
Use ∂x∂xn=nxn−1 to find derivative
∂b∂a=2c×5b4
Solution
∂b∂a=10b4c
Show Solution
Solve the equation
Solve for b
Solve for c
b=2c516ac4
Evaluate
a=2b5c
Rewrite the expression
a=2cb5
Swap the sides of the equation
2cb5=a
Divide both sides
2c2cb5=2ca
Divide the numbers
b5=2ca
Take the 5-th root on both sides of the equation
5b5=52ca
Calculate
b=52ca
Simplify the root
More Steps
Evaluate
52ca
To take a root of a fraction,take the root of the numerator and denominator separately
52c5a
Multiply by the Conjugate
52c×524c45a×524c4
Calculate
2c5a×524c4
Calculate
More Steps
Evaluate
5a×524c4
The product of roots with the same index is equal to the root of the product
5a×24c4
Calculate the product
524ac4
2c524ac4
b=2c524ac4
Solution
More Steps
Evaluate
524ac4
Rewrite the expression
524×5a×5c4
Simplify the root
516ac4
b=2c516ac4
Show Solution