Directional Derivative | Vector Calculus | VTU 1BMATS101 | Q4(a)

Directional Derivative | Vector Calculus | VTU 1BMATS101 (2025 Scheme)

Question:
Find the directional derivative of
f(x, y, z) = 4e^(2x − y + z)
at the point (1, 1, −1) in the direction towards the point (−3, 5, 6).

📝 Question Discussed in the Video
VTU Model Question Paper–I (2025 Scheme)
Subject Code: 1BMATS101 – Calculus & Linear Algebra
Module: 2 – Vector Calculus
Question No.: 4(a)

📘 VTU 1BMATS101 – Model QP–I (2025)
🎓 Calculus & Linear Algebra | VTU 2025
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1BMATS101 | VTU Calculus & Linear Algebra | Model Question Paper–I 2025 Solutions:
👉https://www.youtube.com/playlist?list=PLM9RnGtTy9_9LJxGYqFDpMOlhwYivpCAN
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MODULE 1 – CALCULUS
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Q1(a) Partial Differentiation
👉 https://youtu.be/E6mulwLxBLM
Q1(b) Jacobian
👉 https://youtu.be/GArSusUlIFM
Q1(c) Maxima & Minima
👉 https://youtu.be/4hRGFt34r2o
Q2(a) Chain Rule
👉 https://youtu.be/62iktdBCZwE
Q2(b) Jacobian
👉 https://youtu.be/xx6z6jsJTyU
Q2(c) Maclaurin (2 Variables)
👉 https://youtu.be/4TNwD_DT89M
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MODULE 2 – VECTOR CALCULUS
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Q3(a) Gradient of Dot Product
👉 https://youtu.be/RqZ2_HRjYx8
Q3(b) Irrotational & Scalar Potential
👉 https://youtu.be/v47Dx4c5rDc
Q3(c) Cartesian → Spherical
👉 https://youtu.be/0ApeNnO3rAU
Q4(a) Directional Derivative
👉 https://youtu.be/zhetMtjwl2I
Q4(b) Divergence & Curl
👉 https://youtu.be/WMUuzV4b3Ng
Q4(c) Cartesian → Cylindrical
👉 https://youtu.be/1wfTmva0PL8
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MODULE 3 – LINEAR ALGEBRA
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Q5(a) Rank of Matrix
👉 https://youtu.be/iLt6QxLqQwI
Q5(b) Diagonalization
👉 https://youtu.be/dMMtsZBicgw
Q5(c) Traffic Flow
👉 https://youtu.be/_F9uXRQjsMA
Q6(a) Consistency Test
👉 https://youtu.be/OwSTVeavKrg
Q6(b) Gauss Jordan
👉 https://youtu.be/f-BAr5fteHU
Q6(c) Eigenvalues & Eigenvectors
👉 https://youtu.be/KoJ4sOuRUww
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MODULE 4 – VECTOR SPACE
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Q7(a) Linear Combination
👉 https://youtu.be/E-4HF7ADWFg
Q7(b) Subspace Test
👉 https://youtu.be/MWDwu-KQwKQ
Q7(c) Basis & Dimension (Row/Col/Null)
👉 https://youtu.be/idatYZKtu2Q
Q8(a) Basis & Dimension (Subspace)
👉 https://youtu.be/npSwrdUs8sM
Q8(b) Inner Product
👉 https://youtu.be/JTOsSg_5r-Q
Q8(c) Coordinates w.r.t Basis
👉 https://youtu.be/cmcFtz8yALw
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MODULE 5 – LINEAR TRANSFORMATION
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Q9(a) Linear Transformation | Check Linear or Not
👉 https://youtu.be/c2cpSwTWPN8
Q9(b) Singular Linear Transformation | Kernel
👉 https://youtu.be/K2fBl_UHoeY
Q9(c) Rank and Nullity of Linear Transformation
👉 https://youtu.be/B4YNIkO19LU
Q10(a) Linear Transformation | V₁(R) to V₃(R)
👉 https://youtu.be/XnyifWGXmkE
Q10(b) Matrix of Linear Transformation (Relative to Basis)
👉 https://youtu.be/yeudZ05mRcE
Q10(c) Invertible Linear Transformation | Find F Inverse
👉 https://youtu.be/QnCIf6GtwOc

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MODULE-WISE PLAYLISTS
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Model QP–I (All Modules)
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9LJxGYqFDpMOlhwYivpCAN
Module 1 – Calculus
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_8ULBX0wU4d3y2p8HZA3BeX
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-rqPtcCwDq2MBKGy4pDk6K
Module 2 – Vector Calculus
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_9CcDmlQM7n_q6ABPHD5As-
Module 3 – Linear Algebra
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-rmNJXVPre7KSNkYjG63d5
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-rSzBJZDttMpYRKQYzxTm4
Module 4 – Vector Space
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_88Z1aKoF-xcrhEZ3Z4ElAB
Module 5 – Linear Transformation
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9__fllLHI_SsGvlsurgj-BjE
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